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}}

\int e^{- 3 x} tan (e^{- 3 x}) d x

\int_{2}^{3} \frac{27}{3 - x} d x

\int \frac{5 e ^{x}}{e ^{x} + 4} d x

x \to 8 - lim (\frac{6 x}{x - 8})

f (t) = t^{2} + 1

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