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

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

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

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

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derivative of

\frac{1}{2 x + 3}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x + 3) = 1

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

Simplify

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

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

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

\frac{1}{4}

\frac{d}{d x} (arctan (3 x^{2}))

\int_{0}^{\infty} x e^{- b x} d x

y = \frac{x}{x + 6}, (4, 0.2)

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