What is the derivative of-(4x-3/((2x^2-3x-5)^2)) ?

The derivative of-(4x-3/((2x^2-3x-5)^2)) is -(2(-12x^2+18x-19))/((2x^2-3x-5)^3)

What is the first derivative of-(4x-3/((2x^2-3x-5)^2)) ?

The first derivative of-(4x-3/((2x^2-3x-5)^2)) is -(2(-12x^2+18x-19))/((2x^2-3x-5)^3)

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\frac{d}{d x} (- \frac{4 x - 3}{( 2 x ^{2} - 3 x - 5 ) ^{2}})

- \frac{2 ( - 12 x ^{2} + 18 x - 19 )}{( 2 x ^{2} - 3 x - 5 ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{4 x - 3}{( 2 x ^{2} - 3 x - 5 ) ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (\frac{4 x - 3}{( 2 x ^{2} - 3 x - 5 ) ^{2}})

Apply the Quotient Rule:

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

= - \frac{\frac{d}{d x} ( 4 x - 3 ) ( 2 x ^{2} - 3 x - 5 ) ^{2} - \frac{d}{d x} ( ( 2 x ^{2} - 3 x - 5 ) ^{2} ) ( 4 x - 3 )}{( ( 2 x ^{2} - 3 x - 5 ) ^{2} ) ^{2}}

\frac{d}{d x} (4 x - 3) = 4

\frac{d}{d x} ((2 x^{2} - 3 x - 5)^{2}) = 2 (2 x^{2} - 3 x - 5) (4 x - 3)

= - \frac{4 ( 2 x ^{2} - 3 x - 5 ) ^{2} - 2 ( 2 x ^{2} - 3 x - 5 ) ( 4 x - 3 ) ( 4 x - 3 )}{( ( 2 x ^{2} - 3 x - 5 ) ^{2} ) ^{2}}

Simplify

- \frac{4 ( 2 x ^{2} - 3 x - 5 ) ^{2} - 2 ( 2 x ^{2} - 3 x - 5 ) ( 4 x - 3 ) ( 4 x - 3 )}{( ( 2 x ^{2} - 3 x - 5 ) ^{2} ) ^{2}} : - \frac{2 ( - 12 x ^{2} + 18 x - 19 )}{( 2 x ^{2} - 3 x - 5 ) ^{3}}

= - \frac{2 ( - 12 x ^{2} + 18 x - 19 )}{( 2 x ^{2} - 3 x - 5 ) ^{3}}

\frac{d x}{d y} = - \frac{4 y}{x}

y ln (x) y^{^{'}} = (\frac{y + 1}{x})^{2}

\int 3 cos^{3} (5 x) d x

\frac{e ^{2 x}}{x}

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

What is the derivative of-(4x-3/((2x^2-3x-5)^2)) ?
The derivative of-(4x-3/((2x^2-3x-5)^2)) is -(2(-12x^2+18x-19))/((2x^2-3x-5)^3)
What is the first derivative of-(4x-3/((2x^2-3x-5)^2)) ?
The first derivative of-(4x-3/((2x^2-3x-5)^2)) is -(2(-12x^2+18x-19))/((2x^2-3x-5)^3)