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

The derivative of ln(1+x^2-arcsin(1/x)) is (2x)/(1+x^2)+1/(xsqrt(x^2-1))

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{2 x}{1 + x ^{2}} + \frac{1}{x x ^{2} - 1}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

= \frac{2 x}{1 + x ^{2}} + \frac{1}{x x ^{2} - 1}

\int (12 x^{11} - \frac{11}{x ^{11}}) d x

f (x) = 1 + e^{x}

h \to 0 lim (\frac{5}{h})

\int_{- 2}^{2} π (4 - x^{2})^{2} d x

\frac{\partial}{\partial y} (lo g_{3} (x - y))

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