What is the derivative of 3/(sqrt(1-2x)) ?

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

What is the first derivative of 3/(sqrt(1-2x)) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{0}^{\frac{1}{2}} 8 arccos (x) d x

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\int q^{2} cos (2 q) d q

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

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