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)= x/(x^2-16)

Solution

derivative of

f (x) = \frac{x}{x ^{2} - 16}

Solution

\frac{- x ^{2} - 16}{( x ^{2} - 16 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} - 16})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} ( x ^{2} - 16 ) - \frac{d}{d x} ( x ^{2} - 16 ) x}{( x ^{2} - 16 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} - 16) = 2 x

= \frac{1 \cdot ( x ^{2} - 16 ) - 2 xx}{( x ^{2} - 16 ) ^{2}}

1 \cdot (x^{2} - 16) - 2 xx = - x^{2} - 16

= \frac{- x ^{2} - 16}{( x ^{2} - 16 ) ^{2}}

Popular Examples

limit as x approaches 1 of x/(1-x^4)

x \to 1 lim (\frac{x}{1 - x ^{4}})

area y=(40)/x ,y=-9x+39 area

y = \frac{40}{x}, y = - 9 x + 39

derivative of sqrt(6)x-sqrt(2x)

\frac{d}{d x} (6 x - 2 x)

inverse oflaplace 1/(15s^3)inverse laplace

\frac{1}{15 s ^{3}}

(\partial)/(\partial x)((x-cy)^9+(x+cy)^9)

\frac{\partial}{\partial x} ((x - cy)^{9} + (x + cy)^{9})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x^2-16) ?
The derivative of f(x)= x/(x^2-16) is (-x^2-16)/((x^2-16)^2)
What is the first derivative of f(x)= x/(x^2-16) ?
The first derivative of f(x)= x/(x^2-16) is (-x^2-16)/((x^2-16)^2)