What is the derivative of x(x+4^{1/3}) ?

The derivative of x(x+4^{1/3}) is (4x+12)/(3(x+4)^{2/3)}

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

The first derivative of x(x+4^{1/3}) is (4x+12)/(3(x+4)^{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 (x + 4)^{\frac{1}{3}})

\frac{4 x + 12}{3 ( x + 4 ) ^{\frac{2}{3}}}

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x + 4)^{\frac{1}{3}}

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

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot (x + 4)^{\frac{1}{3}} + \frac{1}{3 ( x + 4 ) ^{\frac{2}{3}}} x : \frac{4 x + 12}{3 ( x + 4 ) ^{\frac{2}{3}}}

= \frac{4 x + 12}{3 ( x + 4 ) ^{\frac{2}{3}}}

x \to 0 - lim (x^{3} + 2 x + 2)

y^{^{'}} = \frac{x}{y} + \frac{y}{x}

y = 6 + 2 x, y = \frac{12 + x}{2}

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

x \to \infty lim (\frac{x}{1})

What is the derivative of x(x+4^{1/3}) ?
The derivative of x(x+4^{1/3}) is (4x+12)/(3(x+4)^{2/3)}
What is the first derivative of x(x+4^{1/3}) ?
The first derivative of x(x+4^{1/3}) is (4x+12)/(3(x+4)^{2/3)}