What is the derivative of (x^5/(4-x^4)) ?

The derivative of (x^5/(4-x^4)) is (20x^4-x^8)/((4-x^4)^2)

What is the first derivative of (x^5/(4-x^4)) ?

The first derivative of (x^5/(4-x^4)) is (20x^4-x^8)/((4-x^4)^2)

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 ^{5}}{4 - x ^{4}})

\frac{20 x ^{4} - x ^{8}}{( 4 - x ^{4} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{5}}{4 - x ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{5} ) ( 4 - x ^{4} ) - \frac{d}{d x} ( 4 - x ^{4} ) x ^{5}}{( 4 - x ^{4} ) ^{2}}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= \frac{5 x ^{4} ( 4 - x ^{4} ) - ( - 4 x ^{3} ) x ^{5}}{( 4 - x ^{4} ) ^{2}}

Simplify

\frac{5 x ^{4} ( 4 - x ^{4} ) - ( - 4 x ^{3} ) x ^{5}}{( 4 - x ^{4} ) ^{2}} : \frac{20 x ^{4} - x ^{8}}{( 4 - x ^{4} ) ^{2}}

= \frac{20 x ^{4} - x ^{8}}{( 4 - x ^{4} ) ^{2}}

\frac{d}{d x} ((5 x)^{9 x})

\frac{d}{d x} (x^{4} + 3 x^{2})

f (x) = x^{4} + 3 x^{3}, at x = 1

n = 1 \sum \infty \frac{2}{5 ^{n - 1}}

\int 2 x e^{x^{2} - 1} d x

What is the derivative of (x^5/(4-x^4)) ?
The derivative of (x^5/(4-x^4)) is (20x^4-x^8)/((4-x^4)^2)
What is the first derivative of (x^5/(4-x^4)) ?
The first derivative of (x^5/(4-x^4)) is (20x^4-x^8)/((4-x^4)^2)