How do you find the derivative of #sqrt(x^5)#?

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Answer 1 · 2017-01-15T15:55:13

#5/2sqrt(x^3)#

Rewrite the function using all fractional exponents and with knowledge of the rule #(x^a)^b=x^(ab)#.

#sqrt(x^5)=(x^5)^(1/2)=x^(5/2)#

We now use the power rule, which says that the derivative of #x^n# is equal to #d/dx(x^n)=nx^(n-1)#.

So, the derivative of #x^(5/2)# is:

#d/dx(x^(5/2))=5/2x^(5/2)=5/2x^(3/2)#

Using the notation you used originally, you may write this as:

#d/dx(x^(5/2))=5/2sqrt(x^3)#