What is the derivative of f(x)=sqrt(x)(x^{-1}+7) ?

The derivative of f(x)=sqrt(x)(x^{-1}+7) is (7x-1)/(2x^{3/2)}

What is the first derivative of f(x)=sqrt(x)(x^{-1}+7) ?

The first derivative of f(x)=sqrt(x)(x^{-1}+7) is (7x-1)/(2x^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = x (x^{- 1} + 7)

\frac{7 x - 1}{2 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (x (x^{- 1} + 7))

Apply the Product Rule:

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

f = x, g = x^{- 1} + 7

= \frac{d}{d x} (x) (x^{- 1} + 7) + \frac{d}{d x} (x^{- 1} + 7) x

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

\frac{d}{d x} (x^{- 1} + 7) = - \frac{1}{x ^{2}}

= \frac{1}{2 x} (x^{- 1} + 7) + (- \frac{1}{x ^{2}}) x

Simplify

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

= \frac{7 x - 1}{2 x ^{\frac{3}{2}}}

\int (y - 4) d y

f (x) = sin (x) ln (x^{4} + \frac{1}{x})

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

\int \frac{27}{27 + e ^{x}} d x

x^{\frac{11}{2}}

What is the derivative of f(x)=sqrt(x)(x^{-1}+7) ?
The derivative of f(x)=sqrt(x)(x^{-1}+7) is (7x-1)/(2x^{3/2)}
What is the first derivative of f(x)=sqrt(x)(x^{-1}+7) ?
The first derivative of f(x)=sqrt(x)(x^{-1}+7) is (7x-1)/(2x^{3/2)}