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Popular >

d/(dθ)(\sqrt[3]{tan(5θ)})

Solution

Solution

\frac{5 sec ^{2} ( 5 θ )}{3 tan ^{\frac{2}{3}} ( 5 θ )}

Solution steps

Apply the chain rule:

\frac{1}{3 ( tan ( 5 θ ) ) ^{\frac{2}{3}}} \frac{d}{d θ} (tan (5 θ))

= \frac{1}{3 ( tan ( 5 θ ) ) ^{\frac{2}{3}}} \frac{d}{d θ} (tan (5 θ))

\frac{d}{d θ} (tan (5 θ)) = sec^{2} (5 θ) \cdot 5

= \frac{1}{3 ( tan ( 5 θ ) ) ^{\frac{2}{3}}} sec^{2} (5 θ) \cdot 5

Simplify

\frac{1}{3 tan ^{\frac{2}{3}} ( 5 θ )} sec^{2} (5 θ) \cdot 5 : \frac{5 sec ^{2} ( 5 θ )}{3 tan ^{\frac{2}{3}} ( 5 θ )}

= \frac{5 sec ^{2} ( 5 θ )}{3 tan ^{\frac{2}{3}} ( 5 θ )}

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Frequently Asked Questions (FAQ)

What is the d/(dθ)(\sqrt[3]{tan(5θ)}) ?
The d/(dθ)(\sqrt[3]{tan(5θ)}) is (5sec^2(5θ))/(3tan^{2/3)(5θ)}
What is the first d/(dθ)(\sqrt[3]{tan(5θ)}) ?
The first d/(dθ)(\sqrt[3]{tan(5θ)}) is (5sec^2(5θ))/(3tan^{2/3)(5θ)}