What is the derivative of ((5x^5-3)/((-3x^3+1))) ?

The derivative of ((5x^5-3)/((-3x^3+1))) is (-30x^7+25x^4-27x^2)/((-3x^3+1)^2)

What is the first derivative of ((5x^5-3)/((-3x^3+1))) ?

The first derivative of ((5x^5-3)/((-3x^3+1))) is (-30x^7+25x^4-27x^2)/((-3x^3+1)^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{( 5 x ^{5} - 3 )}{( - 3 x ^{3} + 1 )})

\frac{- 30 x ^{7} + 25 x ^{4} - 27 x ^{2}}{( - 3 x ^{3} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( 5 x ^{5} - 3 )}{( - 3 x ^{3} + 1 )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x ^{5} - 3 ) ( - 3 x ^{3} + 1 ) - \frac{d}{d x} ( - 3 x ^{3} + 1 ) ( 5 x ^{5} - 3 )}{( - 3 x ^{3} + 1 ) ^{2}}

\frac{d}{d x} (5 x^{5} - 3) = 25 x^{4}

\frac{d}{d x} (- 3 x^{3} + 1) = - 9 x^{2}

= \frac{25 x ^{4} ( - 3 x ^{3} + 1 ) - ( - 9 x ^{2} ) ( 5 x ^{5} - 3 )}{( - 3 x ^{3} + 1 ) ^{2}}

Simplify

\frac{25 x ^{4} ( - 3 x ^{3} + 1 ) - ( - 9 x ^{2} ) ( 5 x ^{5} - 3 )}{( - 3 x ^{3} + 1 ) ^{2}} : \frac{- 30 x ^{7} + 25 x ^{4} - 27 x ^{2}}{( - 3 x ^{3} + 1 ) ^{2}}

= \frac{- 30 x ^{7} + 25 x ^{4} - 27 x ^{2}}{( - 3 x ^{3} + 1 ) ^{2}}

y = 2 (6 x^{2} - 42 x + 49)

f (x) = 25 x

\int_{1}^{e} 3 x^{2} ln (x) d x

f (x) = 3 x^{\frac{1}{2}}

\frac{\partial}{\partial y} (x y - x^{2} y)

What is the derivative of ((5x^5-3)/((-3x^3+1))) ?
The derivative of ((5x^5-3)/((-3x^3+1))) is (-30x^7+25x^4-27x^2)/((-3x^3+1)^2)
What is the first derivative of ((5x^5-3)/((-3x^3+1))) ?
The first derivative of ((5x^5-3)/((-3x^3+1))) is (-30x^7+25x^4-27x^2)/((-3x^3+1)^2)