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Popular >

derivative of (4x+5/(4x-5))

Solution

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

Solution

- \frac{40}{( 4 x - 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{4 ( 4 x - 5 ) - 4 ( 4 x + 5 )}{( 4 x - 5 ) ^{2}} : - \frac{40}{( 4 x - 5 ) ^{2}}

= - \frac{40}{( 4 x - 5 ) ^{2}}

Popular Examples

integral of ((e^x-e^{-x})/(e^x+e^{-x)})

\int (\frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}}) d x

integral of (6x)/((4-3x^2)^4)

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

derivative of ln((x^2+4/(x^2+1)))

\frac{d}{d x} (ln (\frac{x ^{2} + 4}{x ^{2} + 1}))

derivative of x^3-6x^2-15x+4 derivative of

x^{3} - 6 x^{2} - 15 x + 4

limit as x approaches 5 of x^{-2}

x \to 5 lim (x^{- 2})

Frequently Asked Questions (FAQ)

What is the derivative of (4x+5/(4x-5)) ?
The derivative of (4x+5/(4x-5)) is -(40)/((4x-5)^2)
What is the first derivative of (4x+5/(4x-5)) ?
The first derivative of (4x+5/(4x-5)) is -(40)/((4x-5)^2)