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

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

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

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

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

\frac{2 ( 2 x ^{2} - 1 ) ^{3} + 36 x ( 2 x ^{2} - 1 ) ^{2} ( x + 4 )}{3 ( x + 4 ) ^{\frac{1}{3}}}

Solution steps

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

Apply the Product Rule:

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

f = (x + 4)^{\frac{2}{3}}, g = (2 x^{2} - 1)^{3}

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

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

\frac{d}{d x} ((2 x^{2} - 1)^{3}) = 12 x (2 x^{2} - 1)^{2}

= \frac{2}{3 ( x + 4 ) ^{\frac{1}{3}}} (2 x^{2} - 1)^{3} + 12 x (2 x^{2} - 1)^{2} (x + 4)^{\frac{2}{3}}

Simplify

\frac{2}{3 ( x + 4 ) ^{\frac{1}{3}}} (2 x^{2} - 1)^{3} + 12 x (2 x^{2} - 1)^{2} (x + 4)^{\frac{2}{3}} : \frac{2 ( 2 x ^{2} - 1 ) ^{3} + 36 x ( 2 x ^{2} - 1 ) ^{2} ( x + 4 )}{3 ( x + 4 ) ^{\frac{1}{3}}}

= \frac{2 ( 2 x ^{2} - 1 ) ^{3} + 36 x ( 2 x ^{2} - 1 ) ^{2} ( x + 4 )}{3 ( x + 4 ) ^{\frac{1}{3}}}

\frac{1}{( s - 1 ) ^{2} + 4}

f (x) = x^{2} + 1, at x = - 5

\int_{0}^{1} cos (π x) d x

\frac{d ^{4}}{d x ^{4}} (sin (x))

x \to 3 lim (2 x^{3} - 4 x - 2)

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