# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve power rule problems step by step online.

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

Learn how to solve power rule problems step by step online. Find the derivative (d/dx)(x^(-3/2)) using the power rule. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Subtract the values -\frac{3}{2} and -1. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Multiply the fraction and term.

$\frac{-\frac{3}{2}}{\sqrt{x^{5}}}$
$\frac{d}{dx}\left(x^{-1\cdot \frac{3}{2}}\right)$

Power rule

### Time to solve it:

~ 0.02 s (SnapXam)