What is (\partial)/(\partial x)(arcsin(l/x)) ?

The answer to (\partial)/(\partial x)(arcsin(l/x)) is -l/(xsqrt(x^2-l^2))

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(\partial)/(\partial x)(arcsin(l/x))

\frac{\partial}{\partial x} (arcsin (\frac{l}{x}))

- \frac{l}{x x ^{2} - l ^{2}}

Solution steps

\frac{\partial}{\partial x} (arcsin (\frac{l}{x}))

Apply the chain rule:

\frac{1}{1 - ( \frac{l}{x} ) ^{2}} \frac{\partial}{\partial x} (\frac{l}{x})

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

\frac{\partial}{\partial x} (\frac{l}{x}) = - \frac{l}{x ^{2}}

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

Simplify

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

= - \frac{l}{x x ^{2} - l ^{2}}

What is (\partial)/(\partial x)(arcsin(l/x)) ?
The answer to (\partial)/(\partial x)(arcsin(l/x)) is -l/(xsqrt(x^2-l^2))