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

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

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

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

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derivative of

y = 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 )}

y^{^{''}} + 9 y = - sin (3 t)

y = 2 x^{3} + 3 x^{2} - 4 x, y = x^{2}

y^{^{''}} + 4 y^{^{'}} + 34 y = 0

f (x) = \frac{2}{4 x + 3}

\int_{1}^{e^{2}} \frac{ln ^{6} ( x ^{2} )}{x} d x

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