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Popular >

derivative of \sqrt[3]{sin^2(2x})

Solution

Solution

\frac{2 sin ( 4 x )}{3 sin ^{\frac{4}{3}} ( 2 x )}

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (sin^{2} (2 x)) = 2 sin (4 x)

= \frac{1}{3 ( sin ^{2} ( 2 x ) ) ^{\frac{2}{3}}} \cdot 2 sin (4 x)

Simplify

\frac{1}{3 ( sin ^{2} ( 2 x ) ) ^{\frac{2}{3}}} \cdot 2 sin (4 x) : \frac{2 sin ( 4 x )}{3 sin ^{\frac{4}{3}} ( 2 x )}

= \frac{2 sin ( 4 x )}{3 sin ^{\frac{4}{3}} ( 2 x )}

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\int \frac{π}{2} \frac{π}{32} sec (2 θ) tan (2 θ) d θ

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{sin^2(2x}) ?
The derivative of \sqrt[3]{sin^2(2x}) is (2sin(4x))/(3sin^{4/3)(2x)}
What is the first derivative of \sqrt[3]{sin^2(2x}) ?
The first derivative of \sqrt[3]{sin^2(2x}) is (2sin(4x))/(3sin^{4/3)(2x)}