# Example of the Slope of a Tangent

In this tutorial we shall discuss an example of the slope of a tangent to any curve at some given point.

Consider the slope of a tangent to ${x^2} = 16y$ at the point $\left( {4,1} \right)$

We have

Differentiating both sides with respect to $x$, we get

For the slope of the tangent at the given point $\left( {4,1} \right)$, put $x = 4,\,y = 1$ in equation (ii) to get

Thus, the slope of the tangent to ${x^2} = 16y$ at the point $\left( {4,1} \right)$ is $\frac{1}{2}$.