What is the derivative of x^{11}arccos(x) ?

The derivative of x^{11}arccos(x) is 11x^{10}arccos(x)-(x^{11})/(sqrt(1-x^2))

What is the first derivative of x^{11}arccos(x) ?

The first derivative of x^{11}arccos(x) is 11x^{10}arccos(x)-(x^{11})/(sqrt(1-x^2))

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derivative of

x^{11} arccos (x)

11 x^{10} arccos (x) - \frac{x ^{11}}{1 - x ^{2}}

Solution steps

\frac{d}{d x} (x^{11} arccos (x))

Apply the Product Rule:

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

f = x^{11}, g = arccos (x)

= \frac{d}{d x} (x^{11}) arccos (x) + \frac{d}{d x} (arccos (x)) x^{11}

\frac{d}{d x} (x^{11}) = 11 x^{10}

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

= 11 x^{10} arccos (x) + (- \frac{1}{1 - x ^{2}}) x^{11}

Simplify

11 x^{10} arccos (x) + (- \frac{1}{1 - x ^{2}}) x^{11} : 11 x^{10} arccos (x) - \frac{x ^{11}}{1 - x ^{2}}

= 11 x^{10} arccos (x) - \frac{x ^{11}}{1 - x ^{2}}

x^{3} - 8 x^{2} + 18 x - 5, x + 5

\frac{d}{d x} (\frac{3 x + 2}{x ^{2} + 1})

g (x) = e^{x^{5}}, (- 1, \frac{1}{e})

\frac{\partial}{\partial x} (2 ln (x))

t^{2} e^{2 t}

What is the derivative of x^{11}arccos(x) ?
The derivative of x^{11}arccos(x) is 11x^{10}arccos(x)-(x^{11})/(sqrt(1-x^2))
What is the first derivative of x^{11}arccos(x) ?
The first derivative of x^{11}arccos(x) is 11x^{10}arccos(x)-(x^{11})/(sqrt(1-x^2))