en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sqrt(x)(x-3)^2

Solution

derivative of

x (x - 3)^{2}

Solution

\frac{5 x ^{2} - 18 x + 9}{2 x}

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x - 3)^{2}

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

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

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

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

Simplify

\frac{1}{2 x} (x - 3)^{2} + 2 (x - 3) x : \frac{5 x ^{2} - 18 x + 9}{2 x}

= \frac{5 x ^{2} - 18 x + 9}{2 x}

Popular Examples

integral of (x/(sqrt(1+x^2)))

\int (\frac{x}{1 + x ^{2}}) d x

derivative of 3x(sin(x+cos(x)))

\frac{d}{d x} (3 x (sin (x) + cos (x)))

limit as x approaches 5 of (3x+3)/(x-5)

x \to 5 lim (\frac{3 x + 3}{x - 5})

derivative of x^{x-1}derivative of

x^{x - 1}

(\partial)/(\partial x)(xln(z^6+x^4))

\frac{\partial}{\partial x} (x ln (z^{6} + x^{4}))

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)(x-3)^2 ?
The derivative of sqrt(x)(x-3)^2 is (5x^2-18x+9)/(2sqrt(x))
What is the first derivative of sqrt(x)(x-3)^2 ?
The first derivative of sqrt(x)(x-3)^2 is (5x^2-18x+9)/(2sqrt(x))