What is the derivative of (x^{2/3}+3(x^{1/3}+5x)) ?

The derivative of (x^{2/3}+3(x^{1/3}+5x)) is 46/3+(2x^{2/3}+25x^{4/3}+3)/(3x^{2/3)}

What is the first derivative of (x^{2/3}+3(x^{1/3}+5x)) ?

The first derivative of (x^{2/3}+3(x^{1/3}+5x)) is 46/3+(2x^{2/3}+25x^{4/3}+3)/(3x^{2/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{46}{3} + \frac{2 x ^{\frac{2}{3}} + 25 x ^{\frac{4}{3}} + 3}{3 x ^{\frac{2}{3}}}

Solution steps

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

Apply the Product Rule:

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

f = x^{\frac{2}{3}} + 3, g = x^{\frac{1}{3}} + 5 x

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

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

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

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

Simplify

\frac{2}{3 x ^{\frac{1}{3}}} (x^{\frac{1}{3}} + 5 x) + (\frac{1}{3 x ^{\frac{2}{3}}} + 5) (x^{\frac{2}{3}} + 3) : \frac{46}{3} + \frac{2 x ^{\frac{2}{3}} + 25 x ^{\frac{4}{3}} + 3}{3 x ^{\frac{2}{3}}}

= \frac{46}{3} + \frac{2 x ^{\frac{2}{3}} + 25 x ^{\frac{4}{3}} + 3}{3 x ^{\frac{2}{3}}}

\frac{d y}{d x} = \frac{sec ( y )}{( x + 5 ) ^{2}}

\int \frac{1}{x ^{2} x ^{2} - 121} d x

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

\int \frac{x ^{3}}{2 - x ^{2}} d x

\frac{d y}{d x} = \frac{1}{3} x^{3}

What is the derivative of (x^{2/3}+3(x^{1/3}+5x)) ?
The derivative of (x^{2/3}+3(x^{1/3}+5x)) is 46/3+(2x^{2/3}+25x^{4/3}+3)/(3x^{2/3)}
What is the first derivative of (x^{2/3}+3(x^{1/3}+5x)) ?
The first derivative of (x^{2/3}+3(x^{1/3}+5x)) is 46/3+(2x^{2/3}+25x^{4/3}+3)/(3x^{2/3)}