What is the derivative of x/((x^2-1^4)) ?

The derivative of x/((x^2-1^4)) is (-7x^2-1)/((x^2-1)^5)

What is the first derivative of x/((x^2-1^4)) ?

The first derivative of x/((x^2-1^4)) is (-7x^2-1)/((x^2-1)^5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{- 7 x ^{2} - 1}{( x ^{2} - 1 ) ^{5}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((x^{2} - 1)^{4}) = 8 x (x^{2} - 1)^{3}

= \frac{1 \cdot ( x ^{2} - 1 ) ^{4} - 8 x ( x ^{2} - 1 ) ^{3} x}{( ( x ^{2} - 1 ) ^{4} ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{2} - 1 ) ^{4} - 8 x ( x ^{2} - 1 ) ^{3} x}{( ( x ^{2} - 1 ) ^{4} ) ^{2}} : \frac{- 7 x ^{2} - 1}{( x ^{2} - 1 ) ^{5}}

= \frac{- 7 x ^{2} - 1}{( x ^{2} - 1 ) ^{5}}

\int tan^{2} (x) \cdot sec (x) d x

\frac{1}{4} x^{2}, 3 - x, x = 1

\frac{d}{d x} (ln (ln (12 x)))

\int \frac{1}{2 sin ^{2} ( x ) + 3 cos ^{2} ( x )} d x

y^{^{''}} + 81 y = cos (2 t)

What is the derivative of x/((x^2-1^4)) ?
The derivative of x/((x^2-1^4)) is (-7x^2-1)/((x^2-1)^5)
What is the first derivative of x/((x^2-1^4)) ?
The first derivative of x/((x^2-1^4)) is (-7x^2-1)/((x^2-1)^5)