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Derivative of $$$x^{\frac{3}{2}}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(x^{\frac{3}{2}}\right)$$$.
Solution
Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = \frac{3}{2}$$$:
$${\color{red}\left(\frac{d}{dx} \left(x^{\frac{3}{2}}\right)\right)} = {\color{red}\left(\frac{3 \sqrt{x}}{2}\right)}$$Thus, $$$\frac{d}{dx} \left(x^{\frac{3}{2}}\right) = \frac{3 \sqrt{x}}{2}$$$.
Answer
$$$\frac{d}{dx} \left(x^{\frac{3}{2}}\right) = \frac{3 \sqrt{x}}{2}$$$A
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