Step-by-step Solution

Find the derivative $\frac{d}{dx}\left(x^{\frac{-3}{2}}\right)$ using the power rule

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Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(x^{-1\cdot \frac{3}{2}}\right)$

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$\frac{1}{\sqrt{x^{3}}}=y$

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Learn how to solve problems step by step online. Find the derivative (d/dx)(x^(-3/2)) using the power rule. Rearrange the equation. Take the reciprocal of both sides of the equation. Removing the variable's exponent. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}.

Final Answer

$x=\frac{1}{\sqrt[3]{y^{2}}}$