What is the derivative of (-2x^2+25/(sqrt(25-x^2))) ?

The derivative of (-2x^2+25/(sqrt(25-x^2))) is (2x^3-75x)/((25-x^2)sqrt(25-x^2))

What is the first derivative of (-2x^2+25/(sqrt(25-x^2))) ?

The first derivative of (-2x^2+25/(sqrt(25-x^2))) is (2x^3-75x)/((25-x^2)sqrt(25-x^2))

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\frac{d}{d x} (\frac{- 2 x ^{2} + 25}{25 - x ^{2}})

\frac{2 x ^{3} - 75 x}{( 25 - x ^{2} ) 25 - x ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 2 x ^{2} + 25}{25 - x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( - 2 x ^{2} + 25 ) 25 - x ^{2} - \frac{d}{d x} ( 25 - x ^{2} ) ( - 2 x ^{2} + 25 )}{( 25 - x ^{2} ) ^{2}}

\frac{d}{d x} (- 2 x^{2} + 25) = - 4 x

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= \frac{( - 4 x ) 25 - x ^{2} - ( - \frac{x}{25 - x ^{2}} ) ( - 2 x ^{2} + 25 )}{( 25 - x ^{2} ) ^{2}}

Simplify

\frac{( - 4 x ) 25 - x ^{2} - ( - \frac{x}{25 - x ^{2}} ) ( - 2 x ^{2} + 25 )}{( 25 - x ^{2} ) ^{2}} : \frac{2 x ^{3} - 75 x}{( 25 - x ^{2} ) 25 - x ^{2}}

= \frac{2 x ^{3} - 75 x}{( 25 - x ^{2} ) 25 - x ^{2}}

\frac{d}{d θ} (cos^{2} (θ) - sin^{2} (θ))

\frac{d}{d t} (8 t e^{- t})

\int cos (\frac{y}{x}) d x

n = 0 \sum \infty (- \frac{1}{3})^{n}

(x y^{^{'}} - 1) ln (x) = 2 y

What is the derivative of (-2x^2+25/(sqrt(25-x^2))) ?
The derivative of (-2x^2+25/(sqrt(25-x^2))) is (2x^3-75x)/((25-x^2)sqrt(25-x^2))
What is the first derivative of (-2x^2+25/(sqrt(25-x^2))) ?
The first derivative of (-2x^2+25/(sqrt(25-x^2))) is (2x^3-75x)/((25-x^2)sqrt(25-x^2))