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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

= - \frac{1 \cdot 4 - x ^{2} - ( - \frac{x}{4 - x ^{2}} ) x}{( 4 - x ^{2} ) ^{2}}

Simplify

- \frac{1 \cdot 4 - x ^{2} - ( - \frac{x}{4 - x ^{2}} ) x}{( 4 - x ^{2} ) ^{2}} : - \frac{4}{( 4 - x ^{2} ) 4 - x ^{2}}

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

w (z) = 3 z^{7} - 7 z^{3} + 21 z^{2}

\int \frac{1 - 2 x}{1 - 4 x ^{2}} d x

\frac{\partial}{\partial y} (e^{2 y} - y cos (x y))

\int 7 e^{- 0.1 x} d x

\int sin^{2} (x) d x

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