What is the derivative of arcsin(xy) ?

The derivative of arcsin(xy) is (y+x\frac{dy)/(dx)}{sqrt(1-x^2y^2)}

What is the first derivative of arcsin(xy) ?

The first derivative of arcsin(xy) is (y+x\frac{dy)/(dx)}{sqrt(1-x^2y^2)}

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

Simplify

\frac{1}{1 - ( x y ) ^{2}} (y + x \frac{d y}{d x}) : \frac{y + x \frac{d y}{d x}}{1 - x ^{2} y ^{2}}

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

What is the derivative of arcsin(xy) ?
The derivative of arcsin(xy) is (y+x\frac{dy)/(dx)}{sqrt(1-x^2y^2)}
What is the first derivative of arcsin(xy) ?
The first derivative of arcsin(xy) is (y+x\frac{dy)/(dx)}{sqrt(1-x^2y^2)}