What is the derivative of f(x)=(4x+5)/(4x-5) ?

The derivative of f(x)=(4x+5)/(4x-5) is -(40)/((4x-5)^2)

What is the first derivative of f(x)=(4x+5)/(4x-5) ?

The first derivative of f(x)=(4x+5)/(4x-5) is -(40)/((4x-5)^2)

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derivative of

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

- \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}}

\frac{d}{d x} (ln (sin (x)) + cos^{2} (x))

\int \frac{y ^{2} - 81}{y} d y

n = 0 \sum \infty \frac{1}{2 ^{n} + 3 ^{n}}

\int cos (2 n x) d x

9 (t + 1) \frac{d y}{d t} - 7 y = 14 t

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