What is the derivative of y=(5x-3)^4(2x-7)^{-3} ?

The derivative of y=(5x-3)^4(2x-7)^{-3} is (20(5x-3)^3)/((2x-7)^3)-(6(5x-3)^4)/((2x-7)^4)

What is the first derivative of y=(5x-3)^4(2x-7)^{-3} ?

The first derivative of y=(5x-3)^4(2x-7)^{-3} is (20(5x-3)^3)/((2x-7)^3)-(6(5x-3)^4)/((2x-7)^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = (5 x - 3)^{4} (2 x - 7)^{- 3}

\frac{20 ( 5 x - 3 ) ^{3}}{( 2 x - 7 ) ^{3}} - \frac{6 ( 5 x - 3 ) ^{4}}{( 2 x - 7 ) ^{4}}

Solution steps

\frac{d}{d x} ((5 x - 3)^{4} (2 x - 7)^{- 3})

Apply the Product Rule:

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

f = (5 x - 3)^{4}, g = (2 x - 7)^{- 3}

= \frac{d}{d x} ((5 x - 3)^{4}) (2 x - 7)^{- 3} + \frac{d}{d x} ((2 x - 7)^{- 3}) (5 x - 3)^{4}

\frac{d}{d x} ((5 x - 3)^{4}) = 20 (5 x - 3)^{3}

\frac{d}{d x} ((2 x - 7)^{- 3}) = - \frac{6}{( 2 x - 7 ) ^{4}}

= 20 (5 x - 3)^{3} (2 x - 7)^{- 3} + (- \frac{6}{( 2 x - 7 ) ^{4}}) (5 x - 3)^{4}

Simplify

20 (5 x - 3)^{3} (2 x - 7)^{- 3} + (- \frac{6}{( 2 x - 7 ) ^{4}}) (5 x - 3)^{4} : \frac{20 ( 5 x - 3 ) ^{3}}{( 2 x - 7 ) ^{3}} - \frac{6 ( 5 x - 3 ) ^{4}}{( 2 x - 7 ) ^{4}}

= \frac{20 ( 5 x - 3 ) ^{3}}{( 2 x - 7 ) ^{3}} - \frac{6 ( 5 x - 3 ) ^{4}}{( 2 x - 7 ) ^{4}}

\int \frac{5}{27 ( x + 3 )} d x

\frac{d}{d v} (tan (\frac{u}{v}))

\int_{- \frac{π}{9}}^{\frac{π}{9}} 2 sin (3 x) - tan (3 x) d x

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

\int 225 - t^{2} d t

What is the derivative of y=(5x-3)^4(2x-7)^{-3} ?
The derivative of y=(5x-3)^4(2x-7)^{-3} is (20(5x-3)^3)/((2x-7)^3)-(6(5x-3)^4)/((2x-7)^4)
What is the first derivative of y=(5x-3)^4(2x-7)^{-3} ?
The first derivative of y=(5x-3)^4(2x-7)^{-3} is (20(5x-3)^3)/((2x-7)^3)-(6(5x-3)^4)/((2x-7)^4)