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

The derivative of (-x^2/(2x^2-3)) is (6x)/((2x^2-3)^2)

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

The first derivative of (-x^2/(2x^2-3)) is (6x)/((2x^2-3)^2)

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

\frac{6 x}{( 2 x ^{2} - 3 ) ^{2}}

Solution steps

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

Simplify

\frac{- x ^{2}}{2 x ^{2} - 3} : - \frac{x ^{2}}{2 x ^{2} - 3}

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

- \frac{2 x ( 2 x ^{2} - 3 ) - 4 x x ^{2}}{( 2 x ^{2} - 3 ) ^{2}} : \frac{6 x}{( 2 x ^{2} - 3 ) ^{2}}

= \frac{6 x}{( 2 x ^{2} - 3 ) ^{2}}

f^{^{'}} (x) = 7 x^{4} - 9 x^{3} - 4

\frac{\partial}{\partial x} (\frac{x}{x - b})

\int x (sec (x) tan (x)) d x

d er i v a t i v e 4 x^{3} - 6 x^{2}

\int_{5}^{\infty} \frac{1}{x ^{2}} d x

What is the derivative of (-x^2/(2x^2-3)) ?
The derivative of (-x^2/(2x^2-3)) is (6x)/((2x^2-3)^2)
What is the first derivative of (-x^2/(2x^2-3)) ?
The first derivative of (-x^2/(2x^2-3)) is (6x)/((2x^2-3)^2)