Calculus Examples

$D_{x} (2 x^{- \frac{1}{3}} + \frac{3}{x^{\frac{5}{3}}})$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

Simplify each term.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{d}{d D} [D_{x} (2 \frac{1}{x^{\frac{1}{3}}} + \frac{3}{x^{\frac{5}{3}}})]$

Step 2.2

Combine $2$ and $\frac{1}{x^{\frac{1}{3}}}$ .

$\frac{d}{d D} [D_{x} (\frac{2}{x^{\frac{1}{3}}} + \frac{3}{x^{\frac{5}{3}}})]$

Step 3

Since $D_{x} (\frac{2}{x^{\frac{1}{3}}} + \frac{3}{x^{\frac{5}{3}}})$ is constant with respect to $D$ , the derivative of $D_{x} (\frac{2}{x^{\frac{1}{3}}} + \frac{3}{x^{\frac{5}{3}}})$ with respect to $D$ is $0$ .

$0$