What is the derivative of 1/(2sqrt(x+25)) ?

The derivative of 1/(2sqrt(x+25)) is -1/(4(x+25)^{3/2)}

What is the first derivative of 1/(2sqrt(x+25)) ?

The first derivative of 1/(2sqrt(x+25)) is -1/(4(x+25)^{3/2)}

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derivative of

\frac{1}{2 x + 25}

- \frac{1}{4 ( x + 25 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{2 x + 25})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{1}{x + 25})

Apply exponent rule:

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

= \frac{1}{2} \frac{d}{d x} ((x + 25)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 25 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 25)

= - \frac{1}{2 ( x + 25 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 25)

\frac{d}{d x} (x + 25) = 1

= \frac{1}{2} (- \frac{1}{2 ( x + 25 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

\frac{1}{2} (- \frac{1}{2 ( x + 25 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{1}{4 ( x + 25 ) ^{\frac{3}{2}}}

= - \frac{1}{4 ( x + 25 ) ^{\frac{3}{2}}}

\int \frac{19}{x 1 + 2 x} d x

lo g_{4} (e^{2 x})

\frac{d}{d x} (arccos (- \frac{x}{3}))

x \to 0 - lim (\frac{x ^{2}}{6} - \frac{9}{x})

\frac{d}{d x} (x e^{x} sin (x))

What is the derivative of 1/(2sqrt(x+25)) ?
The derivative of 1/(2sqrt(x+25)) is -1/(4(x+25)^{3/2)}
What is the first derivative of 1/(2sqrt(x+25)) ?
The first derivative of 1/(2sqrt(x+25)) is -1/(4(x+25)^{3/2)}