What is the derivative of x^3arccos(x) ?

The derivative of x^3arccos(x) is 3x^2arccos(x)-(x^3)/(sqrt(1-x^2))

What is the first derivative of x^3arccos(x) ?

The first derivative of x^3arccos(x) is 3x^2arccos(x)-(x^3)/(sqrt(1-x^2))

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\frac{d}{d x} (x^{3} arccos (x))

3 x^{2} arccos (x) - \frac{x ^{3}}{1 - x ^{2}}

Solution steps

\frac{d}{d x} (x^{3} arccos (x))

Apply the Product Rule:

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

f = x^{3}, g = arccos (x)

= \frac{d}{d x} (x^{3}) arccos (x) + \frac{d}{d x} (arccos (x)) x^{3}

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

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

= 3 x^{2} arccos (x) + (- \frac{1}{1 - x ^{2}}) x^{3}

Simplify

3 x^{2} arccos (x) + (- \frac{1}{1 - x ^{2}}) x^{3} : 3 x^{2} arccos (x) - \frac{x ^{3}}{1 - x ^{2}}

= 3 x^{2} arccos (x) - \frac{x ^{3}}{1 - x ^{2}}

\frac{d}{d x} (\frac{1}{4} x^{4} - x^{3})

\int_{2}^{\infty} y e^{- 7 y} d y

\int x \cdot e^{- \frac{x}{4}} d x

\int \frac{6 + t + t ^{2}}{t} d t

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + y ^{2}})

What is the derivative of x^3arccos(x) ?
The derivative of x^3arccos(x) is 3x^2arccos(x)-(x^3)/(sqrt(1-x^2))
What is the first derivative of x^3arccos(x) ?
The first derivative of x^3arccos(x) is 3x^2arccos(x)-(x^3)/(sqrt(1-x^2))