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Popular >

derivative of 3arccos(x/2)

Solution

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

Solution

- \frac{3}{4 - x ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

3 - \frac{1}{1 - ( \frac{x}{2} ) ^{2}} \cdot \frac{1}{2} : - \frac{3}{4 - x ^{2}}

= - \frac{3}{4 - x ^{2}}

Popular Examples

integral of (42w^7-7w)/(7w^5)

\int \frac{42 w ^{7} - 7 w}{7 w ^{5}} d w

limit as x approaches 2 of (x^3-8)/(x+2)

x \to 2 lim (\frac{x ^{3} - 8}{x + 2})

slope ofintercept (4,0),(-2,4)slope intercept

(4, 0), (- 2, 4)

y^{''}+4y^'+3y=4e^{-t},y(0)=0,y^'(0)=2

y^{^{''}} + 4 y^{^{'}} + 3 y = 4 e^{- t}, y (0) = 0, y^{^{'}} (0) = 2

derivative of 1/(sqrt(sin(x)))

\frac{d}{d x} (\frac{1}{sin ( x )})

Frequently Asked Questions (FAQ)

What is the derivative of 3arccos(x/2) ?
The derivative of 3arccos(x/2) is -3/(sqrt(4-x^2))
What is the first derivative of 3arccos(x/2) ?
The first derivative of 3arccos(x/2) is -3/(sqrt(4-x^2))