What is the derivative of 1/(2sqrt(x+12)) ?

The derivative of 1/(2sqrt(x+12)) is -1/(4(x+12)^{3/2)}

What is the first derivative of 1/(2sqrt(x+12)) ?

The first derivative of 1/(2sqrt(x+12)) is -1/(4(x+12)^{3/2)}

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\frac{d}{d x} (\frac{1}{2 x + 12})

- \frac{1}{4 ( x + 12 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{2 x + 12})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{1}{x + 12})

Apply exponent rule:

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

= \frac{1}{2} \frac{d}{d x} ((x + 12)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 12 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 12)

= - \frac{1}{2 ( x + 12 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 12)

\frac{d}{d x} (x + 12) = 1

= \frac{1}{2} (- \frac{1}{2 ( x + 12 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

\frac{1}{2} (- \frac{1}{2 ( x + 12 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{1}{4 ( x + 12 ) ^{\frac{3}{2}}}

= - \frac{1}{4 ( x + 12 ) ^{\frac{3}{2}}}

\frac{\partial}{\partial x} (\frac{x \cdot d}{n \cdot L ( x , d )})

\frac{\partial}{\partial x} (x y + z)

\frac{d}{d t} ((t (y^{2} + y))^{- 1})

\int \frac{9 e ^{9 t}}{3 + e ^{9 t}} d t

\frac{d}{d x} (1 - 5 x)

What is the derivative of 1/(2sqrt(x+12)) ?
The derivative of 1/(2sqrt(x+12)) is -1/(4(x+12)^{3/2)}
What is the first derivative of 1/(2sqrt(x+12)) ?
The first derivative of 1/(2sqrt(x+12)) is -1/(4(x+12)^{3/2)}