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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

= \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

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

Simplify

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

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

\int (x + 4) ln (x) d x

n = 1 \sum \infty 6 (0.9)^{n - 1}

\int - 4 cos (x) - x d x

\frac{d}{d x} ((5 x^{3} - 3 x + 4)^{20})

y^{^{'}} = 7 y^{5}

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