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

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

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

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

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derivative of

f (x) = 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}}

\frac{\partial}{\partial y} (sin (y) + y sin (x))

x \to 5 - lim (3)

y^{^{''}} = x^{2} - 1

5^{x}

\int 3 x - 4 d x

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