What is the derivative of 9x^{1/3}+9/2 x^{4/3} ?

The derivative of 9x^{1/3}+9/2 x^{4/3} is (3+6x)/(x^{2/3)}

What is the first derivative of 9x^{1/3}+9/2 x^{4/3} ?

The first derivative of 9x^{1/3}+9/2 x^{4/3} is (3+6x)/(x^{2/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

9 x^{\frac{1}{3}} + \frac{9}{2} x^{\frac{4}{3}}

\frac{3 + 6 x}{x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (9 x^{\frac{1}{3}} + \frac{9}{2} x^{\frac{4}{3}})

Simplify

9 x^{\frac{1}{3}} + \frac{9}{2} x^{\frac{4}{3}} : 9 x^{\frac{1}{3}} + \frac{9 x ^{\frac{4}{3}}}{2}

= \frac{d}{d x} (9 x^{\frac{1}{3}} + \frac{9 x ^{\frac{4}{3}}}{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (9 x^{\frac{1}{3}}) + \frac{d}{d x} (\frac{9 x ^{\frac{4}{3}}}{2})

\frac{d}{d x} (9 x^{\frac{1}{3}}) = \frac{3}{x ^{\frac{2}{3}}}

\frac{d}{d x} (\frac{9 x ^{\frac{4}{3}}}{2}) = 6 x^{\frac{1}{3}}

= \frac{3}{x ^{\frac{2}{3}}} + 6 x^{\frac{1}{3}}

Simplify

\frac{3}{x ^{\frac{2}{3}}} + 6 x^{\frac{1}{3}} : \frac{3 + 6 x}{x ^{\frac{2}{3}}}

= \frac{3 + 6 x}{x ^{\frac{2}{3}}}

\frac{\partial}{\partial x} (- x e^{(x y)})

\int - 2 x + 18 x^{2} - 4 x^{3} + C d x

\int 2 cos^{3} (x) sin (x) d x

\frac{d}{d x} (2 x x sin (x))

\int (2 cos (x))^{2} d x

What is the derivative of 9x^{1/3}+9/2 x^{4/3} ?
The derivative of 9x^{1/3}+9/2 x^{4/3} is (3+6x)/(x^{2/3)}
What is the first derivative of 9x^{1/3}+9/2 x^{4/3} ?
The first derivative of 9x^{1/3}+9/2 x^{4/3} is (3+6x)/(x^{2/3)}