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

The derivative of ((4x-4^5)/((2x-5)^7)) is (4(4x-4)^4(-4x-11))/((2x-5)^8)

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

The first derivative of ((4x-4^5)/((2x-5)^7)) is (4(4x-4)^4(-4x-11))/((2x-5)^8)

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

\frac{4 ( 4 x - 4 ) ^{4} ( - 4 x - 11 )}{( 2 x - 5 ) ^{8}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((2 x - 5)^{7}) = 14 (2 x - 5)^{6}

= \frac{20 ( 4 x - 4 ) ^{4} ( 2 x - 5 ) ^{7} - 14 ( 2 x - 5 ) ^{6} ( 4 x - 4 ) ^{5}}{( ( 2 x - 5 ) ^{7} ) ^{2}}

Simplify

\frac{20 ( 4 x - 4 ) ^{4} ( 2 x - 5 ) ^{7} - 14 ( 2 x - 5 ) ^{6} ( 4 x - 4 ) ^{5}}{( ( 2 x - 5 ) ^{7} ) ^{2}} : \frac{4 ( 4 x - 4 ) ^{4} ( - 4 x - 11 )}{( 2 x - 5 ) ^{8}}

= \frac{4 ( 4 x - 4 ) ^{4} ( - 4 x - 11 )}{( 2 x - 5 ) ^{8}}

38 e^{x^{2}} x

\int \frac{7}{5 - 6 x} d x

\frac{1}{2} x^{2} + 2 x - 2 + 35 x^{- 1}

\frac{d}{d x} (ln (e^{x} - e^{- x}))

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

What is the derivative of ((4x-4^5)/((2x-5)^7)) ?
The derivative of ((4x-4^5)/((2x-5)^7)) is (4(4x-4)^4(-4x-11))/((2x-5)^8)
What is the first derivative of ((4x-4^5)/((2x-5)^7)) ?
The first derivative of ((4x-4^5)/((2x-5)^7)) is (4(4x-4)^4(-4x-11))/((2x-5)^8)