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

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

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

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

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derivative of

\frac{1}{1 + 4 x}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d t} (\frac{t + π}{t} cos (t))

x \to 0 lim (\frac{1}{x ^{2}} - \frac{1}{x})

\int 2 t + 1 d t

\int sec^{6} (3 x) d x

y^{^{'}} - \frac{4 y}{t} = 5

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