What is the derivative of sqrt(x)(x^3-1)^6 ?

The derivative of sqrt(x)(x^3-1)^6 is ((x^3-1)^6)/(2sqrt(x))+18x^2sqrt(x)(x^3-1)^5

What is the first derivative of sqrt(x)(x^3-1)^6 ?

The first derivative of sqrt(x)(x^3-1)^6 is ((x^3-1)^6)/(2sqrt(x))+18x^2sqrt(x)(x^3-1)^5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

x (x^{3} - 1)^{6}

\frac{( x ^{3} - 1 ) ^{6}}{2 x} + 18 x^{2} x (x^{3} - 1)^{5}

Solution steps

\frac{d}{d x} (x (x^{3} - 1)^{6})

Apply the Product Rule:

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

f = x, g = (x^{3} - 1)^{6}

= \frac{d}{d x} (x) (x^{3} - 1)^{6} + \frac{d}{d x} ((x^{3} - 1)^{6}) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} ((x^{3} - 1)^{6}) = 18 x^{2} (x^{3} - 1)^{5}

= \frac{1}{2 x} (x^{3} - 1)^{6} + 18 x^{2} (x^{3} - 1)^{5} x

\frac{1}{2 x} (x^{3} - 1)^{6} = \frac{( x ^{3} - 1 ) ^{6}}{2 x}

= \frac{( x ^{3} - 1 ) ^{6}}{2 x} + 18 x^{2} x (x^{3} - 1)^{5}

\int \frac{1}{x ^{2} + 8 x + 97} d x

\int e^{7 x} cos (5 x) d x

\frac{\partial}{\partial x} (y cos (4 x))

\frac{d}{d t} (a sin (γ t) + b cos (γ t))

\int (x^{2} + 3 x)^{2} (2 x + 3) d x

What is the derivative of sqrt(x)(x^3-1)^6 ?
The derivative of sqrt(x)(x^3-1)^6 is ((x^3-1)^6)/(2sqrt(x))+18x^2sqrt(x)(x^3-1)^5
What is the first derivative of sqrt(x)(x^3-1)^6 ?
The first derivative of sqrt(x)(x^3-1)^6 is ((x^3-1)^6)/(2sqrt(x))+18x^2sqrt(x)(x^3-1)^5