What is the derivative of (3x+1/(2x-5)) ?

The derivative of (3x+1/(2x-5)) is -(17)/((2x-5)^2)

What is the first derivative of (3x+1/(2x-5)) ?

The first derivative of (3x+1/(2x-5)) is -(17)/((2x-5)^2)

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\frac{d}{d x} (\frac{3 x + 1}{2 x - 5})

- \frac{17}{( 2 x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x + 1}{2 x - 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x + 1 ) ( 2 x - 5 ) - \frac{d}{d x} ( 2 x - 5 ) ( 3 x + 1 )}{( 2 x - 5 ) ^{2}}

\frac{d}{d x} (3 x + 1) = 3

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

= \frac{3 ( 2 x - 5 ) - 2 ( 3 x + 1 )}{( 2 x - 5 ) ^{2}}

Simplify

\frac{3 ( 2 x - 5 ) - 2 ( 3 x + 1 )}{( 2 x - 5 ) ^{2}} : - \frac{17}{( 2 x - 5 ) ^{2}}

= - \frac{17}{( 2 x - 5 ) ^{2}}

\int_{b}^{2 b} x^{4} d x

\frac{d}{d x} (x^{3} e^{- 3 x})

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

\int sin^{2} (2 θ) d θ

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} + 12 y = 0

What is the derivative of (3x+1/(2x-5)) ?
The derivative of (3x+1/(2x-5)) is -(17)/((2x-5)^2)
What is the first derivative of (3x+1/(2x-5)) ?
The first derivative of (3x+1/(2x-5)) is -(17)/((2x-5)^2)