What is the derivative of sqrt(1-x^2)arccos(x) ?

The derivative of sqrt(1-x^2)arccos(x) is -(xarccos(x))/(sqrt(1-x^2))-1

What is the first derivative of sqrt(1-x^2)arccos(x) ?

The first derivative of sqrt(1-x^2)arccos(x) is -(xarccos(x))/(sqrt(1-x^2))-1

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

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

Solution steps

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

Apply the Product Rule:

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

f = 1 - x^{2}, g = arccos (x)

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

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

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

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

Simplify

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

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

What is the derivative of sqrt(1-x^2)arccos(x) ?
The derivative of sqrt(1-x^2)arccos(x) is -(xarccos(x))/(sqrt(1-x^2))-1
What is the first derivative of sqrt(1-x^2)arccos(x) ?
The first derivative of sqrt(1-x^2)arccos(x) is -(xarccos(x))/(sqrt(1-x^2))-1