What is the derivative of ln(1+sqrt(x)) ?

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

What is the first derivative of ln(1+sqrt(x)) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

n = 1 \sum \infty (sin (9))^{n}

49 y^{^{''}} + 14 y^{^{'}} + y = 0

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

\int_{- 2}^{1} (8 x^{3} - 3 x^{2}) d x

\frac{d y}{d x} = 3 x e^{y}

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