What is the derivative of \sqrt[3]{cos(x^3}) ?

The derivative of \sqrt[3]{cos(x^3}) is -x^2sin(x^3)sec^{2/3}(x^3)

What is the first derivative of \sqrt[3]{cos(x^3}) ?

The first derivative of \sqrt[3]{cos(x^3}) is -x^2sin(x^3)sec^{2/3}(x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

- x^{2} sin (x^{3}) sec^{\frac{2}{3}} (x^{3})

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (cos (x^{3})) = - sin (x^{3}) \cdot 3 x^{2}

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

Simplify

\frac{1}{3 cos ^{\frac{2}{3}} ( x ^{3} )} (- sin (x^{3}) \cdot 3 x^{2}) : - x^{2} sin (x^{3}) sec^{\frac{2}{3}} (x^{3})

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

\int_{0}^{1} x (1 - x) sin (nπ x) d x

x^{- 7}

\int_{1}^{\infty} 3 x e^{- x} d x

\int tanh^{2} (3 x) d x

n = 0 \sum \infty n \cdot a^{n}

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