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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = ln (x + 1)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to \infty lim (- 3 x^{4})

\int tan^{2} (x se) c^{10} x d x

\int 2 1 - e^{- x} e^{- x} d x

- 5 cos (0.4 t)

y^{^{'}} = y^{2}

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