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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{2}{( 2 - x ) ^{3}} \frac{d}{d x} (2 - x)

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

\frac{d}{d x} (2 - x) = - 1

= 2 (- \frac{2}{( 2 - x ) ^{3}} (- 1))

Simplify

2 (- \frac{2}{( 2 - x ) ^{3}} (- 1)) : \frac{4}{( 2 - x ) ^{3}}

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

\frac{d}{d x} (\frac{2}{3} (x^{2} - 1)^{\frac{3}{2}})

\frac{d}{d x} (arctan (5 x^{2} - 1))

\int x^{3} x^{2} + 9 d x

\frac{\partial}{\partial x} (sin (π (6 x - y)))

arctan (\frac{1 + t}{1 - t})

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