What is the derivative of-1/(2sqrt(1-x)) ?

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

What is the first derivative of-1/(2sqrt(1-x)) ?

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

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derivative of

- \frac{1}{2 1 - x}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= - \frac{1}{2} \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

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

Simplify

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

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

\int 1 + t^{4} d t

t \to 0 lim (e^{- 6 t})

\int \frac{x ^{2} - 16}{x ( x + 2 ) ^{3}} d x

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

t^{2} y^{^{''}} - 2 y = 3 t^{2} - 1

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