What is the derivative of 1/(\sqrt[3]{a+bx^3}) ?

The derivative of 1/(\sqrt[3]{a+bx^3}) is -(bx^2)/((a+bx^3)^{4/3)}

What is the first derivative of 1/(\sqrt[3]{a+bx^3}) ?

The first derivative of 1/(\sqrt[3]{a+bx^3}) is -(bx^2)/((a+bx^3)^{4/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

- \frac{b x ^{2}}{( a + b x ^{3} ) ^{\frac{4}{3}}}

Solution steps

Apply exponent rule:

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

= \frac{d}{d x} ((a + b x^{3})^{- \frac{1}{3}})

Apply the chain rule:

- \frac{1}{3 ( a + b x ^{3} ) ^{\frac{4}{3}}} \frac{d}{d x} (a + b x^{3})

= - \frac{1}{3 ( a + b x ^{3} ) ^{\frac{4}{3}}} \frac{d}{d x} (a + b x^{3})

\frac{d}{d x} (a + b x^{3}) = 3 b x^{2}

= - \frac{1}{3 ( a + b x ^{3} ) ^{\frac{4}{3}}} \cdot 3 b x^{2}

Simplify

- \frac{1}{3 ( a + b x ^{3} ) ^{\frac{4}{3}}} \cdot 3 b x^{2} : - \frac{b x ^{2}}{( a + b x ^{3} ) ^{\frac{4}{3}}}

= - \frac{b x ^{2}}{( a + b x ^{3} ) ^{\frac{4}{3}}}

x \to 0 + lim (x ln (x^{4}))

\frac{\partial}{\partial x} (x ln (\frac{x ^{2}}{y ^{3}}))

\int_{- 2}^{3} \frac{26}{x ^{4}} d x

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

\frac{d}{d x} (4 sec (x) - 8 cos (x))

What is the derivative of 1/(\sqrt[3]{a+bx^3}) ?
The derivative of 1/(\sqrt[3]{a+bx^3}) is -(bx^2)/((a+bx^3)^{4/3)}
What is the first derivative of 1/(\sqrt[3]{a+bx^3}) ?
The first derivative of 1/(\sqrt[3]{a+bx^3}) is -(bx^2)/((a+bx^3)^{4/3)}