What is (\partial)/(\partial x)(xarccos(x)) ?

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

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(\partial)/(\partial x)(xarccos(x))

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

arccos (x) - \frac{x}{1 - x ^{2}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arccos (x)

= \frac{\partial}{\partial x} (x) arccos (x) + \frac{\partial}{\partial x} (arccos (x)) x

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

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

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

Simplify

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

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

\int cos (x) \cdot x d x

\int \frac{2 d t}{t ^{2}} d x

\frac{10}{s ^{2} + 2 \cdot s + 10}

\int \frac{x ^{2}}{x ^{3} - 1} d x

\frac{d}{d x} (ln (x + 7))

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