What is the derivative of ln(sqrt(x+3)) ?

The derivative of ln(sqrt(x+3)) is 1/(2(x+3))

What is the first derivative of ln(sqrt(x+3)) ?

The first derivative of ln(sqrt(x+3)) is 1/(2(x+3))

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derivative of

ln (x + 3)

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

Solution steps

\frac{d}{d x} (ln (x + 3))

Apply the chain rule:

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

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

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

= \frac{1}{x + 3} \cdot \frac{1}{2 x + 3}

Simplify

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

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

\int \frac{e ^{\frac{2}{x}}}{x ^{2}} d x

y^{^{'}} + 6 y = 4 x^{3} e^{- 6 x}

\frac{d y}{d x} = 5 + e^{y - 5 x + 1}, y (0) = - 1

x \to 2 + lim (- 1)

\frac{d}{d x} (8 x + x^{2} + 7 x + 3)

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