en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of \sqrt[3]{t^2}+2sqrt(t^3)

Solution

derivative of

3 t^{2} + 2 t^{3}

Solution

\frac{2 t}{3 ( t ^{2} ) ^{\frac{2}{3}}} + 3 t

Solution steps

\frac{d}{d t} (3 t^{2} + 2 t^{3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{2 t}{3 ( t ^{2} ) ^{\frac{2}{3}}} + 3 t

Graph

Popular Examples

integral from 0 to 1 of (2x)/((x^2+2)^2)

\int_{0}^{1} \frac{2 x}{( x ^{2} + 2 ) ^{2}} d x

(\partial)/(\partial x)(7e^{5x})

\frac{\partial}{\partial x} (7 e^{5 x})

f (x) = e^{x^{2} - 4}

(\partial)/(\partial x)(x^2+y^2-4y)

\frac{\partial}{\partial x} (x^{2} + y^{2} - 4 y)

derivative of (2x)/(x^2-4)

d er i v a t i v e \frac{2 x}{x ^{2} - 4}

Frequently Asked Questions (FAQ)

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