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Popular >

derivative of (2x+5/(2x-5))

Solution

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

Solution

- \frac{20}{( 2 x - 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( 2 x - 5 ) - 2 ( 2 x + 5 )}{( 2 x - 5 ) ^{2}} : - \frac{20}{( 2 x - 5 ) ^{2}}

= - \frac{20}{( 2 x - 5 ) ^{2}}

Popular Examples

(\partial)/(\partial x)(sqrt(26-x^2-y^2))

\frac{\partial}{\partial x} (26 - x^{2} - y^{2})

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\frac{d}{d x} (sec (x^{2} - 1))

laplacetransform (t-1)^4 laplace transform

(t - 1)^{4}

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

(\partial)/(\partial x)(sqrt(25-x^2))

\frac{\partial}{\partial x} (25 - x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of (2x+5/(2x-5)) ?
The derivative of (2x+5/(2x-5)) is -(20)/((2x-5)^2)
What is the first derivative of (2x+5/(2x-5)) ?
The first derivative of (2x+5/(2x-5)) is -(20)/((2x-5)^2)