What is the derivative of 5/(\sqrt[4]{(x^3+2)^3)} ?

The derivative of 5/(\sqrt[4]{(x^3+2)^3)} is -(45x^2(x^3+2)^2)/(4((x^3+2)^3)^{5/4)}

What is the first derivative of 5/(\sqrt[4]{(x^3+2)^3)} ?

The first derivative of 5/(\sqrt[4]{(x^3+2)^3)} is -(45x^2(x^3+2)^2)/(4((x^3+2)^3)^{5/4)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

- \frac{45 x ^{2} ( x ^{3} + 2 ) ^{2}}{4 ( ( x ^{3} + 2 ) ^{3} ) ^{\frac{5}{4}}}

Solution steps

Take the constant out:

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

Apply exponent rule:

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

= 5 \frac{d}{d x} (((x^{3} + 2)^{3})^{- \frac{1}{4}})

Apply the chain rule:

- \frac{1}{4 ( ( x ^{3} + 2 ) ^{3} ) ^{\frac{5}{4}}} \frac{d}{d x} ((x^{3} + 2)^{3})

= - \frac{1}{4 ( ( x ^{3} + 2 ) ^{3} ) ^{\frac{5}{4}}} \frac{d}{d x} ((x^{3} + 2)^{3})

\frac{d}{d x} ((x^{3} + 2)^{3}) = 9 x^{2} (x^{3} + 2)^{2}

= 5 - \frac{1}{4 ( ( x ^{3} + 2 ) ^{3} ) ^{\frac{5}{4}}} \cdot 9 x^{2} (x^{3} + 2)^{2}

Simplify

5 - \frac{1}{4 ( ( x ^{3} + 2 ) ^{3} ) ^{\frac{5}{4}}} \cdot 9 x^{2} (x^{3} + 2)^{2} : - \frac{45 x ^{2} ( x ^{3} + 2 ) ^{2}}{4 ( ( x ^{3} + 2 ) ^{3} ) ^{\frac{5}{4}}}

= - \frac{45 x ^{2} ( x ^{3} + 2 ) ^{2}}{4 ( ( x ^{3} + 2 ) ^{3} ) ^{\frac{5}{4}}}

x \to 4 lim (16)

\frac{d}{d x} (\frac{2 x - 1}{x + 1})

x \to \infty lim (x^{7})

\int cos (30) d x

\int f (x) d x

What is the derivative of 5/(\sqrt[4]{(x^3+2)^3)} ?
The derivative of 5/(\sqrt[4]{(x^3+2)^3)} is -(45x^2(x^3+2)^2)/(4((x^3+2)^3)^{5/4)}
What is the first derivative of 5/(\sqrt[4]{(x^3+2)^3)} ?
The first derivative of 5/(\sqrt[4]{(x^3+2)^3)} is -(45x^2(x^3+2)^2)/(4((x^3+2)^3)^{5/4)}