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))

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\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}

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))