How do you differentiate #-x^(2+1)#?

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Answer 1 · 2017-07-02T02:39:04

#d/(dx) -x^(2+1) = color(blue)(-3x^2#

We're asked to find the derivative of the expression

#-x^(2+1)#

This can be written as

#d/(dx) (-x^3)#

We can first factor out the constant, #-1#:

#-1(d/(dx) x^3)#

Using the power rule:

#d/(dx) x^n = nx^(n-1)#

#d/(dx) x^3 = 3x^(3-1) = 3x^2#

Lastly, multiplying by #-1# gives

#d/(dx) -x^3 = color(blue)(-3x^2#