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

The answer to (\partial)/(\partial x)(arcsin(x/l)) is 1/(sqrt(l^2-x^2))

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (\frac{x}{l}) = \frac{1}{l}

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

Simplify

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

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

\frac{d}{d x} (\frac{3}{5 x ^{\frac{2}{5}}})

\int (\frac{e ^{x}}{2} + x x) d x

y^{^{'}} = \frac{4 x ^{7} e ^{\frac{y}{x}} + x ^{5} y ^{2}}{x ^{6} y}

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

What is (\partial)/(\partial x)(arcsin(x/l)) ?
The answer to (\partial)/(\partial x)(arcsin(x/l)) is 1/(sqrt(l^2-x^2))