What is the derivative of 1/(3tan^3(x)) ?

The derivative of 1/(3tan^3(x)) is -cot^4(x)sec^2(x)

What is the first derivative of 1/(3tan^3(x)) ?

The first derivative of 1/(3tan^3(x)) is -cot^4(x)sec^2(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{1}{3 tan ^{3} ( x )}

- cot^{4} (x) sec^{2} (x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{1}{3} \frac{d}{d x} (tan^{- 3} (x))

Apply the chain rule:

- \frac{3}{( tan ( x ) ) ^{4}} \frac{d}{d x} (tan (x))

= - \frac{3}{( tan ( x ) ) ^{4}} \frac{d}{d x} (tan (x))

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= \frac{1}{3} (- \frac{3}{( tan ( x ) ) ^{4}} sec^{2} (x))

Simplify

\frac{1}{3} (- \frac{3}{tan ^{4} ( x )} sec^{2} (x)) : - cot^{4} (x) sec^{2} (x)

= - cot^{4} (x) sec^{2} (x)

(x + 2)^{- 4}

\frac{d}{d y} (2 y)

\frac{1}{( 3 x + 4 ) ^{3}}

1 - 1 - x^{2}

f (x) = (3 x - 4) 2 (x - 2)

What is the derivative of 1/(3tan^3(x)) ?
The derivative of 1/(3tan^3(x)) is -cot^4(x)sec^2(x)
What is the first derivative of 1/(3tan^3(x)) ?
The first derivative of 1/(3tan^3(x)) is -cot^4(x)sec^2(x)