en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x^2-4/(x^2))

Solution

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2}})

Solution

\frac{8}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 4 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{2} - 4 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{2} - 4) = 2 x

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

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

Simplify

\frac{2 x x ^{2} - 2 x ( x ^{2} - 4 )}{( x ^{2} ) ^{2}} : \frac{8}{x ^{3}}

= \frac{8}{x ^{3}}

Popular Examples

tangent of f(x)=e^{4x},\at x= 1/4 ln(5)tangent of

f (x) = e^{4 x}, at x = \frac{1}{4} ln (5)

area f(x)=2sin(x)+sin(2x),y=0,0<= x<= pi area

f (x) = 2 sin (x) + sin (2 x), y = 0, 0 \leq x \leq π

x^{^{'}} = x - 15

derivative of 2/((2+x^3))

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

(d^3)/(dx^3)(4/x)

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

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-4/(x^2)) ?
The derivative of (x^2-4/(x^2)) is 8/(x^3)
What is the first derivative of (x^2-4/(x^2)) ?
The first derivative of (x^2-4/(x^2)) is 8/(x^3)