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Popular >

derivative of f(x)=(arccos(x))^3

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of cos(3x+2)

\int cos (3 x + 2) d x

tangent of f(x)=4(x-1/x)^3,\at x=2 tangent of

f (x) = 4 (x - \frac{1}{x})^{3}, at x = 2

tangent of y=(-2x)/(x^2+1),(0,0)tangent of

y = \frac{- 2 x}{x ^{2} + 1}, (0, 0)

area f(x)=-5/(x^3),y=0,x=-4,x=-1 area

f (x) = - \frac{5}{x ^{3}}, y = 0, x = - 4, x = - 1

limit as x approaches 0 of x/(csc^2(x))

x \to 0 lim (\frac{x}{csc ^{2} ( x )})

Frequently Asked Questions (FAQ)

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