What is the derivative of x^{4/5}(x-3^2) ?

The derivative of x^{4/5}(x-3^2) is (14x^2-54x+36)/(5x^{1/5)}

What is the first derivative of x^{4/5}(x-3^2) ?

The first derivative of x^{4/5}(x-3^2) is (14x^2-54x+36)/(5x^{1/5)}

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{4}{5}} (x - 3)^{2})

\frac{14 x ^{2} - 54 x + 36}{5 x ^{\frac{1}{5}}}

Solution steps

\frac{d}{d x} (x^{\frac{4}{5}} (x - 3)^{2})

Apply the Product Rule:

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

f = x^{\frac{4}{5}}, g = (x - 3)^{2}

= \frac{d}{d x} (x^{\frac{4}{5}}) (x - 3)^{2} + \frac{d}{d x} ((x - 3)^{2}) x^{\frac{4}{5}}

\frac{d}{d x} (x^{\frac{4}{5}}) = \frac{4}{5 x ^{\frac{1}{5}}}

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

= \frac{4}{5 x ^{\frac{1}{5}}} (x - 3)^{2} + 2 (x - 3) x^{\frac{4}{5}}

Simplify

\frac{4}{5 x ^{\frac{1}{5}}} (x - 3)^{2} + 2 (x - 3) x^{\frac{4}{5}} : \frac{14 x ^{2} - 54 x + 36}{5 x ^{\frac{1}{5}}}

= \frac{14 x ^{2} - 54 x + 36}{5 x ^{\frac{1}{5}}}

(- 4) (0.2)

\int sec^{8} (2 x) tan (2 x) d x

f (x) = \frac{2 x}{( x + 1 ) ^{2}}, at x = 0

(2.4) (6.6)

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

What is the derivative of x^{4/5}(x-3^2) ?
The derivative of x^{4/5}(x-3^2) is (14x^2-54x+36)/(5x^{1/5)}
What is the first derivative of x^{4/5}(x-3^2) ?
The first derivative of x^{4/5}(x-3^2) is (14x^2-54x+36)/(5x^{1/5)}