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

The derivative of (x^2/(sqrt(4-x^2))) is (8x-x^3)/((4-x^2)sqrt(4-x^2))

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

The first derivative of (x^2/(sqrt(4-x^2))) is (8x-x^3)/((4-x^2)sqrt(4-x^2))

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

\frac{8 x - x ^{3}}{( 4 - x ^{2} ) 4 - x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x 4 - x ^{2} - ( - \frac{x}{4 - x ^{2}} ) x ^{2}}{( 4 - x ^{2} ) ^{2}} : \frac{8 x - x ^{3}}{( 4 - x ^{2} ) 4 - x ^{2}}

= \frac{8 x - x ^{3}}{( 4 - x ^{2} ) 4 - x ^{2}}

- \frac{24}{x ^{4}}

\int p (p + 3)^{6} d p

x \to 4 lim (x - 4)

x \to 5 lim (25 - x^{2})

\int \frac{sin ( 2 x )}{24 + cos ^{2} ( x )} d x

What is the derivative of (x^2/(sqrt(4-x^2))) ?
The derivative of (x^2/(sqrt(4-x^2))) is (8x-x^3)/((4-x^2)sqrt(4-x^2))
What is the first derivative of (x^2/(sqrt(4-x^2))) ?
The first derivative of (x^2/(sqrt(4-x^2))) is (8x-x^3)/((4-x^2)sqrt(4-x^2))