What is the derivative of \sqrt[4]{1+tan(t)} ?

The derivative of \sqrt[4]{1+tan(t)} is (sec^2(t))/(4(1+tan(t))^{3/4)}

What is the first derivative of \sqrt[4]{1+tan(t)} ?

The first derivative of \sqrt[4]{1+tan(t)} is (sec^2(t))/(4(1+tan(t))^{3/4)}

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derivative of

4 1 + tan (t)

\frac{sec ^{2} ( t )}{4 ( 1 + tan ( t ) ) ^{\frac{3}{4}}}

Solution steps

\frac{d}{d t} (4 1 + tan (t))

Apply the chain rule:

\frac{1}{4 ( 1 + tan ( t ) ) ^{\frac{3}{4}}} \frac{d}{d t} (1 + tan (t))

= \frac{1}{4 ( 1 + tan ( t ) ) ^{\frac{3}{4}}} \frac{d}{d t} (1 + tan (t))

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

= \frac{1}{4 ( 1 + tan ( t ) ) ^{\frac{3}{4}}} sec^{2} (t)

Simplify

\frac{1}{4 ( 1 + tan ( t ) ) ^{\frac{3}{4}}} sec^{2} (t) : \frac{sec ^{2} ( t )}{4 ( 1 + tan ( t ) ) ^{\frac{3}{4}}}

= \frac{sec ^{2} ( t )}{4 ( 1 + tan ( t ) ) ^{\frac{3}{4}}}

\int \frac{x ^{2} - x + 28}{x ^{3} + 7 x} d x

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n = 1 \sum \infty \frac{1}{1 + 3 ^{n}}

x d y = 4 y d x

\int x^{2} (- 2)^{5} + x^{2} d x

What is the derivative of \sqrt[4]{1+tan(t)} ?
The derivative of \sqrt[4]{1+tan(t)} is (sec^2(t))/(4(1+tan(t))^{3/4)}
What is the first derivative of \sqrt[4]{1+tan(t)} ?
The first derivative of \sqrt[4]{1+tan(t)} is (sec^2(t))/(4(1+tan(t))^{3/4)}