# How do you find the slope of the tangent line y=x^3 at x=1?

Dec 18, 2016

3

#### Explanation:

The gradient (or slope) of the tangent to a curve at any particular point is given by the derivative at that point

If $y = {x}^{3}$ then $\frac{\mathrm{dy}}{\mathrm{dx}} = 3 {x}^{2}$

When $x = 1 \implies \frac{\mathrm{dy}}{\mathrm{dx}} = 3$

So the slope equals 3