How do you find the second derivative of y=x^5?

1 Answer
Feb 12, 2017

\frac{d^2}{dx^2}(y)=20x^3

Explanation:

Let us examine the equation at hand,
y=x^5

Now, one elemental equation of derivative calculus is that
frac{d}{dx}(y)=mx^(m-1)
when ofcourse y=x^m

Here, m=5 so substituting for m gives us
frac{d}{dx}(y)=5x^4

But we have been asked for the second derivative, this means we are to differentiate the equation again. We've already done it once, so let's do it again.

\frac{d^2}{dx^2}=5*4x^3

The simplified answer can be found thus.