What is the derivative of y=\sqrt[3]{tan(3t)} ?

The derivative of y=\sqrt[3]{tan(3t)} is sec^2(3t)cot^{2/3}(3t)

What is the first derivative of y=\sqrt[3]{tan(3t)} ?

The first derivative of y=\sqrt[3]{tan(3t)} is sec^2(3t)cot^{2/3}(3t)

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derivative of

y = 3 tan (3 t)

sec^{2} (3 t) cot^{\frac{2}{3}} (3 t)

Solution steps

\frac{d}{d t} (3 tan (3 t))

Apply the chain rule:

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

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

\frac{d}{d t} (tan (3 t)) = sec^{2} (3 t) \cdot 3

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

Simplify

\frac{1}{3 tan ^{\frac{2}{3}} ( 3 t )} sec^{2} (3 t) \cdot 3 : sec^{2} (3 t) cot^{\frac{2}{3}} (3 t)

= sec^{2} (3 t) cot^{\frac{2}{3}} (3 t)

cot^{2} (cos (θ))

\frac{d}{d x} (arcsin (6 x^{4}))

\frac{d}{d x} (\frac{x ^{2}}{3} + \frac{5 x}{7} - \frac{8}{5})

f (x) = 5 x^{3}, at x = - 2

\frac{\partial}{\partial x} (x arcsin (x) y)

What is the derivative of y=\sqrt[3]{tan(3t)} ?
The derivative of y=\sqrt[3]{tan(3t)} is sec^2(3t)cot^{2/3}(3t)
What is the first derivative of y=\sqrt[3]{tan(3t)} ?
The first derivative of y=\sqrt[3]{tan(3t)} is sec^2(3t)cot^{2/3}(3t)