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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{2 x ( 2 x - 5 ) ^{2} - 4 ( 2 x - 5 ) ( x ^{2} - 1 )}{( ( 2 x - 5 ) ^{2} ) ^{2}}

Simplify

\frac{2 x ( 2 x - 5 ) ^{2} - 4 ( 2 x - 5 ) ( x ^{2} - 1 )}{( ( 2 x - 5 ) ^{2} ) ^{2}} : \frac{2 ( - 5 x + 2 )}{( 2 x - 5 ) ^{3}}

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

\frac{d}{d x} (4 cos (sin (3 x)))

y^{^{'''}} + y^{^{'}} = t^{2}

t \to 0 lim (\frac{sin ( 4 t )}{t})

d er i v a t i v e 65 x^{\frac{9}{10}}

\int cos (x) csc^{6} (x) d x

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