What is the derivative of y=(2x+5)^5(4x+5)^{-4} ?

The derivative of y=(2x+5)^5(4x+5)^{-4} is (10(2x+5)^4)/((4x+5)^4)-(16(2x+5)^5)/((4x+5)^5)

What is the first derivative of y=(2x+5)^5(4x+5)^{-4} ?

The first derivative of y=(2x+5)^5(4x+5)^{-4} is (10(2x+5)^4)/((4x+5)^4)-(16(2x+5)^5)/((4x+5)^5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = (2 x + 5)^{5} (4 x + 5)^{- 4}

\frac{10 ( 2 x + 5 ) ^{4}}{( 4 x + 5 ) ^{4}} - \frac{16 ( 2 x + 5 ) ^{5}}{( 4 x + 5 ) ^{5}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (2 x + 5)^{5}, g = (4 x + 5)^{- 4}

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

\frac{d}{d x} ((2 x + 5)^{5}) = 10 (2 x + 5)^{4}

\frac{d}{d x} ((4 x + 5)^{- 4}) = - \frac{16}{( 4 x + 5 ) ^{5}}

= 10 (2 x + 5)^{4} (4 x + 5)^{- 4} + (- \frac{16}{( 4 x + 5 ) ^{5}}) (2 x + 5)^{5}

Simplify

10 (2 x + 5)^{4} (4 x + 5)^{- 4} + (- \frac{16}{( 4 x + 5 ) ^{5}}) (2 x + 5)^{5} : \frac{10 ( 2 x + 5 ) ^{4}}{( 4 x + 5 ) ^{4}} - \frac{16 ( 2 x + 5 ) ^{5}}{( 4 x + 5 ) ^{5}}

= \frac{10 ( 2 x + 5 ) ^{4}}{( 4 x + 5 ) ^{4}} - \frac{16 ( 2 x + 5 ) ^{5}}{( 4 x + 5 ) ^{5}}

\frac{d y}{d x} = \frac{x ^{6} - 4 y}{x}

\frac{d y}{d x} = 2 x (x - 2)

\frac{\partial}{\partial x} (\frac{1}{1 + e ^{- w^{T} x}})

\frac{d}{d x} (\frac{2 x}{sec ( x )})

\frac{d}{d x} (A e^{x} + B x e^{x})

What is the derivative of y=(2x+5)^5(4x+5)^{-4} ?
The derivative of y=(2x+5)^5(4x+5)^{-4} is (10(2x+5)^4)/((4x+5)^4)-(16(2x+5)^5)/((4x+5)^5)
What is the first derivative of y=(2x+5)^5(4x+5)^{-4} ?
The first derivative of y=(2x+5)^5(4x+5)^{-4} is (10(2x+5)^4)/((4x+5)^4)-(16(2x+5)^5)/((4x+5)^5)