## Derivative of Sine Square Root of X

In trigonometric differentiation, most of the examples are based on the sine square roots function. We will discuss the derivative… Click here to read more

From basic to higher mathematics

In trigonometric differentiation, most of the examples are based on the sine square roots function. We will discuss the derivative… Click here to read more

In this tutorial we will discuss the basic formulas of differentiation for trigonometric functions. 1. $$\frac{d}{{dx}}\sin x = \cos x$$… Click here to read more

In this tutorial we shall discuss the derivative of inverse trigonometric functions and first we shall prove the sine inverse… Click here to read more

In this tutorial we shall discuss the derivative of inverse trigonometric functions and first we shall prove the cosine inverse… Click here to read more

In this tutorial we shall explore the derivative of inverse trigonometric functions and we shall prove the derivative of tangent… Click here to read more

In this tutorial we shall explore the derivative of inverse trigonometric functions and we shall prove the derivative of cotangent… Click here to read more

In this tutorial we shall explore the derivative of inverse trigonometric functions and we shall prove the derivative of secant… Click here to read more

In this tutorial we shall explore the derivative of inverse trigonometric functions and we shall prove the derivative of cosecant… Click here to read more

In this tutorial we shall discuss the basic formulas of differentiation for inverse trigonometric functions. 1. $$\frac{d}{{dx}}{\sin ^{ –… Click here to read more

A function defined by $$y = {\log _a}x,\,\,\,x > 0$$, where $$x = {a^y},\,\,\,a > 0$$, $$a \ne 1$$ is… Click here to read more

If $$y = f\left( x \right)$$ is a complicated function, i.e. it involves several products of functions, quotients or radical… Click here to read more

In this tutorial we shall discuss the basic differentiation formulas of logarithmic functions. 1. $$\frac{d}{{dx}}\ln x = \frac{1}{x},\,\,\,x >… Click here to read more

Example: Differentiate $${\log _{10}}\left( {\frac{{x + 1}}{x}} \right)$$ with respect to $$x$$. Consider the function \[y = {\log _{10}}\left( {\frac{{x… Click here to read more

In this tutorial we shall find the general rules of derivative of exponential functions, and we shall prove the general… Click here to read more

In this tutorial we shall find the derivative of exponential function $${e^x}$$ and we shall prove the general rules for… Click here to read more

In this tutorial we discuss the basic differentiation formulas of exponential functions. 1. $$\frac{d}{{dx}}{a^x} = \frac{1}{{x\ln a}},\,\,\,a > 0,\,\,\,a \ne… Click here to read more

Example: Differentiate $${a^{\sin x}} + {e^{\cos x}}$$ with respect to $$x$$. We have the given function \[y = {a^{\sin x}}… Click here to read more

In this tutorial we shall study certain combinations of $${e^x}$$ and $${e^{ – x}}$$, which are called hyperbolic functions. These… Click here to read more

In this tutorial we shall prove the derivative of the hyperbolic sine function. Let the function be of the form… Click here to read more

In this tutorial we shall prove the derivative of the hyperbolic cosine function. Let the function be of the form… Click here to read more

In this tutorial we shall prove the derivative of the hyperbolic tangent function. Let the function be of the form… Click here to read more

In this tutorial we shall prove the derivative of the hyperbolic cotangent function. Let the function be of the form… Click here to read more

In this tutorial we shall prove the derivative of the hyperbolic secant function. Let the function be of the form… Click here to read more

In this tutorial we shall prove the derivative of the hyperbolic cosecant function. Let the function be of the form… Click here to read more

In this tutorial we shall discuss the basic formulas of differentiation for hyperbolic functions. 1. $$\frac{d}{{dx}}\sinh x = \cosh x$$… Click here to read more

Example: Differentiate $${x^3}{\tanh ^2}\sqrt x $$ with respect to $$x$$. Consider the function \[y = {x^3}{\tanh ^2}\sqrt x \] Differentiating… Click here to read more

In this tutorial we shall discuss the derivative of the inverse hyperbolic sine function with an example. Let the function… Click here to read more

In this tutorial we shall discuss the derivative of the inverse hyperbolic cosine function with an example. Let the function… Click here to read more

In this tutorial we shall discuss the derivative of the inverse hyperbolic tangent function with an example. Let the function… Click here to read more

In this tutorial we shall discuss the derivative of the inverse hyperbolic secant function with an example. Let the function… Click here to read more

In this tutorial we shall discuss the derivative of the inverse hyperbolic cosecant function with an example. Let the function… Click here to read more

In this tutorial we shall discuss basic formulas of differentiation for inverse hyperbolic functions. 1. $$\frac{d}{{dx}}{\sinh ^{ – 1}}x =… Click here to read more

Example: Differentiate $${\cosh ^{ – 1}}\left( {{x^2} + 1} \right)$$ with respect to $$x$$. Consider the function \[y = {\cosh… Click here to read more

Implicit Function If the independent and the dependent variables are mixed up in such a way that the dependent variable… Click here to read more

Example: Find $$\frac{{dy}}{{dx}}$$, if the given implicit function is \[{x^3} + {y^3} = xy\] We have the given implicit function… Click here to read more

In this tutorial we shall find the higher order derivatives. We have already seen how differentiation is applied to a… Click here to read more

Parametric Function A function in which $$x$$ and $$y$$ are expressed as a function of a third variable is called… Click here to read more

Example: Find the second derivative $${y_2}$$ if $$y = \cos \left( {ax + b} \right)$$. We have the given function… Click here to read more

In this tutorial we shall derive the series expansion of $${e^x}$$ by using Maclaurin’s series expansion function. Consider the function… Click here to read more

In this tutorial we shall derive the series expansion of the trigonometric function sine by using Maclaurin’s series expansion function…. Click here to read more

In this tutorial we shall derive the series expansion of the trigonometric function cosine by using Maclaurin’s series expansion function…. Click here to read more

In this tutorial we shall derive the series expansion of the trigonometric function $$\ln \left( {1 – x} \right)$$ by… Click here to read more

In this tutorial we shall derive the series expansion of the trigonometric function $$\ln \left( {1 + x} \right)$$ by… Click here to read more

In this tutorial we shall derive the series expansion of the trigonometric function $${a^x}$$ by using Maclaurin’s series expansion function…. Click here to read more

In this tutorial we shall derive the series expansion of the trigonometric function $${\tan ^{ – 1}}x$$ by using Maclaurin’s… Click here to read more

In this tutorial we shall derive the series expansion of the hyperbolic sine function by using Maclaurin’s series expansion function…. Click here to read more

In this tutorial we shall derive the series expansion of the hyperbolic cosine function by using Maclaurin’s series expansion function…. Click here to read more