Question

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

Answer 1

`\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.