What is the derivative of f(x)=(2x+5)/(3x-2) ?

The derivative of f(x)=(2x+5)/(3x-2) is -(19)/((3x-2)^2)

What is the first derivative of f(x)=(2x+5)/(3x-2) ?

The first derivative of f(x)=(2x+5)/(3x-2) is -(19)/((3x-2)^2)

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derivative of

f (x) = \frac{2 x + 5}{3 x - 2}

- \frac{19}{( 3 x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 5}{3 x - 2})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (3 x - 2) = 3

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

Simplify

\frac{2 ( 3 x - 2 ) - 3 ( 2 x + 5 )}{( 3 x - 2 ) ^{2}} : - \frac{19}{( 3 x - 2 ) ^{2}}

= - \frac{19}{( 3 x - 2 ) ^{2}}

\frac{\partial}{\partial y} (y^{2} e^{2 x})

\frac{d}{d x} (\frac{- π x ^{2} - 4 x ^{2} + 64 x}{8})

(x - 1) y^{^{''}} - x y^{^{'}} + y = 0

k = 1 \sum \infty \frac{5}{2 ^{k}}

\frac{d y}{d x} = e^{x} + y

What is the derivative of f(x)=(2x+5)/(3x-2) ?
The derivative of f(x)=(2x+5)/(3x-2) is -(19)/((3x-2)^2)
What is the first derivative of f(x)=(2x+5)/(3x-2) ?
The first derivative of f(x)=(2x+5)/(3x-2) is -(19)/((3x-2)^2)