What is the derivative of $\sqrt{x^{3}}$ $sqrt(x^3)$ ?

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Answer 1 · 2015-04-13T08:53:13

To solve this problem you can use the chain rule.

$f (x) = \sqrt{x^{3}} = {(x^{3})}^{\frac{1}{2}}$ $f(x)= sqrt(x^3) = (x^3)^(1/2)$

$f'(x) = 1/2(x^3)^(-1/2)3x^2 = (3/2x^2)(x^(-3/2)) = 3/2x^(2-3/2) = 3/2x^(1/2) = (3sqrt(x))/2$

What is the derivative of sqrt(x^3)√x3sqrt(x^3)?