What is the derivative of \sqrt[3]{x^2}(x^2+1) ?

The derivative of \sqrt[3]{x^2}(x^2+1) is (2x(x^2+1))/(3(x^2)^{2/3)}+2x\sqrt[3]{x^2}

What is the first derivative of \sqrt[3]{x^2}(x^2+1) ?

The first derivative of \sqrt[3]{x^2}(x^2+1) is (2x(x^2+1))/(3(x^2)^{2/3)}+2x\sqrt[3]{x^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

3 x^{2} (x^{2} + 1)

\frac{2 x ( x ^{2} + 1 )}{3 ( x ^{2} ) ^{\frac{2}{3}}} + 2 x 3 x^{2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x^{2}, g = x^{2} + 1

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

n = 1 \sum \infty \frac{8}{5 ^{n - 1}}

\frac{d}{d θ} (r (θ)), r (θ) = cos (θ) cot (θ)

f (x) = (x^{3} + 2) (x^{5} + 7 x^{2} + 3)

\frac{d}{d x} (\frac{x + 2}{x ^{2} + 5 x + 6})

f (x) = 2 + 5 x

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