What is the derivative of sqrt(x)(x^3+x^2-3x) ?

The derivative of sqrt(x)(x^3+x^2-3x) is (7x^2sqrt(x)+5xsqrt(x)-9sqrt(x))/2

What is the first derivative of sqrt(x)(x^3+x^2-3x) ?

The first derivative of sqrt(x)(x^3+x^2-3x) is (7x^2sqrt(x)+5xsqrt(x)-9sqrt(x))/2

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^{3} + x^{2} - 3 x))

\frac{7 x ^{2} x + 5 x x - 9 x}{2}

Solution steps

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

Apply the Product Rule:

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

f = x, g = x^{3} + x^{2} - 3 x

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

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

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

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

Simplify

\frac{1}{2 x} (x^{3} + x^{2} - 3 x) + (3 x^{2} + 2 x - 3) x : \frac{7 x ^{2} x + 5 x x - 9 x}{2}

= \frac{7 x ^{2} x + 5 x x - 9 x}{2}

\int \frac{2 x + 3}{x ^{3} + 3 x} d x

\frac{d}{d x} (\frac{4 x}{4 + x})

\int \frac{1}{e ^{x} + 2} d x

\frac{d}{d x} (e^{- x^{2}} - sin (x) cos (x))

\frac{\partial}{\partial x} (ln (2 x^{3} + y))

What is the derivative of sqrt(x)(x^3+x^2-3x) ?
The derivative of sqrt(x)(x^3+x^2-3x) is (7x^2sqrt(x)+5xsqrt(x)-9sqrt(x))/2
What is the first derivative of sqrt(x)(x^3+x^2-3x) ?
The first derivative of sqrt(x)(x^3+x^2-3x) is (7x^2sqrt(x)+5xsqrt(x)-9sqrt(x))/2