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Derivative of $x^{\frac{3}{2}}$

The calculator will find the derivative of

x^{\frac{3}{2}}

, with steps shown.

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