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

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

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

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

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derivative of

f (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}}

\int cos^{5} (x s i) n^{4} x

w

\int 3 x^{\frac{5}{2}} d x

\int (12 x + 3 x^{4}) (10 x^{2} + x^{5} - 2)^{6} d x

x \to 0 lim (3 x^{2} + x)

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