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)=(8x-7)^{1/2}

Solution

derivative of

f (x) = (8 x - 7)^{\frac{1}{2}}

Solution

\frac{4}{( 8 x - 7 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((8 x - 7)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( 8 x - 7 ) ^{\frac{1}{2}}} \frac{d}{d x} (8 x - 7)

= \frac{1}{2 ( 8 x - 7 ) ^{\frac{1}{2}}} \frac{d}{d x} (8 x - 7)

\frac{d}{d x} (8 x - 7) = 8

= \frac{1}{2 ( 8 x - 7 ) ^{\frac{1}{2}}} \cdot 8

Simplify

\frac{1}{2 ( 8 x - 7 ) ^{\frac{1}{2}}} \cdot 8 : \frac{4}{( 8 x - 7 ) ^{\frac{1}{2}}}

= \frac{4}{( 8 x - 7 ) ^{\frac{1}{2}}}

Popular Examples

(dy)/(dx)=e^{4x+5y}

\frac{d y}{d x} = e^{4 x + 5 y}

integral from 3 to 5 of (y^2)/2+1/(2y^2)

\int_{3}^{5} \frac{y ^{2}}{2} + \frac{1}{2 y ^{2}} d y

integral of x^3-3x^{-4}-2

\int x^{3} - 3 x^{- 4} - 2 d x

integral of x^2log_{e}(x)

\int x^{2} lo g_{e} (x) d x

\frac{d y}{d t} = y + 1

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(8x-7)^{1/2} ?
The derivative of f(x)=(8x-7)^{1/2} is 4/((8x-7)^{1/2)}
What is the first derivative of f(x)=(8x-7)^{1/2} ?
The first derivative of f(x)=(8x-7)^{1/2} is 4/((8x-7)^{1/2)}