en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=sqrt(x)(x-10)

Solution

derivative of

f (x) = x (x - 10)

Solution

\frac{3 x - 10}{2 x}

Solution steps

\frac{d}{d x} (x (x - 10))

Apply the Product Rule:

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

f = x, g = x - 10

= \frac{d}{d x} (x) (x - 10) + \frac{d}{d x} (x - 10) x

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

\frac{d}{d x} (x - 10) = 1

= \frac{1}{2 x} (x - 10) + 1 \cdot x

Simplify

\frac{1}{2 x} (x - 10) + 1 \cdot x : \frac{3 x - 10}{2 x}

= \frac{3 x - 10}{2 x}

Popular Examples

5y^{''}+32y=0,y(0)=8,y^'(0)=5

5 y^{^{''}} + 32 y = 0, y (0) = 8, y^{^{'}} (0) = 5

integral of 1/2 xcos(x^2)

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

integral of 3/(x^3)

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

laplacetransform f(t)=cos(5t)+sin(2t)laplace transform

f (t) = cos (5 t) + sin (2 t)

y^{''}-y=0,y(0)=6

y^{^{''}} - y = 0, y (0) = 6

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x)(x-10) ?
The derivative of f(x)=sqrt(x)(x-10) is (3x-10)/(2sqrt(x))
What is the first derivative of f(x)=sqrt(x)(x-10) ?
The first derivative of f(x)=sqrt(x)(x-10) is (3x-10)/(2sqrt(x))