What is the derivative of 4/(sqrt(1-x)) ?

The derivative of 4/(sqrt(1-x)) is 2/((1-x)^{3/2)}

What is the first derivative of 4/(sqrt(1-x)) ?

The first derivative of 4/(sqrt(1-x)) is 2/((1-x)^{3/2)}

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\frac{d}{d x} (\frac{4}{1 - x})

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

Solution steps

\frac{d}{d x} (\frac{4}{1 - x})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{1 - x})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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7 t^{2}

\int_{- \frac{π}{4}}^{\frac{π}{4}} cos (x) d x

(6 x^{2} + 7) (x^{2} - \frac{1}{x})

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What is the derivative of 4/(sqrt(1-x)) ?
The derivative of 4/(sqrt(1-x)) is 2/((1-x)^{3/2)}
What is the first derivative of 4/(sqrt(1-x)) ?
The first derivative of 4/(sqrt(1-x)) is 2/((1-x)^{3/2)}