What is the derivative of (-7x^2/(2x^2-5)) ?

The derivative of (-7x^2/(2x^2-5)) is (70x)/((2x^2-5)^2)

What is the first derivative of (-7x^2/(2x^2-5)) ?

The first derivative of (-7x^2/(2x^2-5)) is (70x)/((2x^2-5)^2)

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\frac{d}{d x} (\frac{- 7 x ^{2}}{2 x ^{2} - 5})

\frac{70 x}{( 2 x ^{2} - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 7 x ^{2}}{2 x ^{2} - 5})

Simplify

\frac{- 7 x ^{2}}{2 x ^{2} - 5} : - \frac{7 x ^{2}}{2 x ^{2} - 5}

= \frac{d}{d x} (- \frac{7 x ^{2}}{2 x ^{2} - 5})

Take the constant out:

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

= - 7 \frac{d}{d x} (\frac{x ^{2}}{2 x ^{2} - 5})

Apply the Quotient Rule:

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

= - 7 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( 2 x ^{2} - 5 ) - \frac{d}{d x} ( 2 x ^{2} - 5 ) x ^{2}}{( 2 x ^{2} - 5 ) ^{2}}

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

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

= - 7 \cdot \frac{2 x ( 2 x ^{2} - 5 ) - 4 x x ^{2}}{( 2 x ^{2} - 5 ) ^{2}}

Simplify

- 7 \cdot \frac{2 x ( 2 x ^{2} - 5 ) - 4 x x ^{2}}{( 2 x ^{2} - 5 ) ^{2}} : \frac{70 x}{( 2 x ^{2} - 5 ) ^{2}}

= \frac{70 x}{( 2 x ^{2} - 5 ) ^{2}}

What is the derivative of (-7x^2/(2x^2-5)) ?
The derivative of (-7x^2/(2x^2-5)) is (70x)/((2x^2-5)^2)
What is the first derivative of (-7x^2/(2x^2-5)) ?
The first derivative of (-7x^2/(2x^2-5)) is (70x)/((2x^2-5)^2)