What is (\partial)/(\partial x)(arccos(xy)) ?

The answer to (\partial)/(\partial x)(arccos(xy)) is -y/(sqrt(1-x^2y^2))

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(\partial)/(\partial x)(arccos(xy))

\frac{\partial}{\partial x} (arccos (x y))

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

Solution steps

\frac{\partial}{\partial x} (arccos (x y))

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x y) = y

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{m}{p} + 625 \frac{p}{x})

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

\frac{\partial}{\partial x} (\frac{m c T}{wp ( m , T , w , x )})

\int_{0}^{π} π^{25} sin^{2} (x) d x

\int 1 d θ

What is (\partial)/(\partial x)(arccos(xy)) ?
The answer to (\partial)/(\partial x)(arccos(xy)) is -y/(sqrt(1-x^2y^2))