en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arcsin(ln(x))

Solution

\frac{d}{d x} (arcsin (ln (x)))

Solution

\frac{1}{x 1 - ln ^{2} ( x )}

Solution steps

\frac{d}{d x} (arcsin (ln (x)))

Apply the chain rule:

\frac{1}{1 - ( ln ( x ) ) ^{2}} \frac{d}{d x} (ln (x))

= \frac{1}{1 - ( ln ( x ) ) ^{2}} \frac{d}{d x} (ln (x))

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

= \frac{1}{1 - ( ln ( x ) ) ^{2}} \cdot \frac{1}{x}

Simplify

\frac{1}{1 - ln ^{2} ( x )} \cdot \frac{1}{x} : \frac{1}{x 1 - ln ^{2} ( x )}

= \frac{1}{x 1 - ln ^{2} ( x )}

Popular Examples

inverse oflaplace 1/(s^2-3s+2)inverse laplace

\frac{1}{s ^{2} - 3 s + 2}

derivative of arctan(sqrt(5x^2-1))derivative of

arctan (5 x^{2} - 1)

(d^2y)/(dx^2)+2(dy)/(dx)=1+9x^2

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 1 + 9 x^{2}

integral of 3sec^4(x)

\int 3 sec^{4} (x) d x

limit as x approaches (3pi)/4 of-2sec(x)

x \to \frac{3 π}{4} lim (- 2 sec (x))

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(ln(x)) ?
The derivative of arcsin(ln(x)) is 1/(xsqrt(1-ln^2(x)))
What is the first derivative of arcsin(ln(x)) ?
The first derivative of arcsin(ln(x)) is 1/(xsqrt(1-ln^2(x)))