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.