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

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

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

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

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derivative of

ln (3 + x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} + y = e^{4 x}

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

x \to 3 lim (3 x - 7)

\frac{1}{x ^{7}}

x \to 0 + lim (e^{x} - (1 + x))

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