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Popular >

derivative of (sin(x)^{1/3})

Solution

\frac{d}{d x} ((sin (x))^{\frac{1}{3}})

Solution

\frac{cos ( x )}{3 sin ^{\frac{2}{3}} ( x )}

Solution steps

\frac{d}{d x} ((sin (x))^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( sin ( x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (sin (x))

= \frac{1}{3 ( sin ( x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{1}{3 ( sin ( x ) ) ^{\frac{2}{3}}} cos (x)

Simplify

\frac{1}{3 sin ^{\frac{2}{3}} ( x )} cos (x) : \frac{cos ( x )}{3 sin ^{\frac{2}{3}} ( x )}

= \frac{cos ( x )}{3 sin ^{\frac{2}{3}} ( x )}

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Frequently Asked Questions (FAQ)

What is the derivative of (sin(x)^{1/3}) ?
The derivative of (sin(x)^{1/3}) is (cos(x))/(3sin^{2/3)(x)}
What is the first derivative of (sin(x)^{1/3}) ?
The first derivative of (sin(x)^{1/3}) is (cos(x))/(3sin^{2/3)(x)}