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Popular >

derivative of arccos(x/2)

Solution

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

Solution

- \frac{1}{4 - x ^{2}}

Solution steps

\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}

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

Simplify

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

= - \frac{1}{4 - x ^{2}}

Popular Examples

derivative of f(-1)=4x^2+4x-3 derivative of

f (- 1) = 4 x^{2} + 4 x - 3

derivative of f(x)=((sqrt(x))/(x+1))^2 derivative of

f (x) = (\frac{x}{x + 1})^{2}

(\partial)/(\partial y)(e^x(1-cos(y)))

\frac{\partial}{\partial y} (e^{x} (1 - cos (y)))

inverse oflaplace 4/(s-2)inverse laplace

\frac{4}{s - 2}

y^'=((x^2+3y^2))/(2xy)

y^{^{'}} = \frac{( x ^{2} + 3 y ^{2} )}{2 x y}

Frequently Asked Questions (FAQ)

What is the derivative of arccos(x/2) ?
The derivative of arccos(x/2) is -1/(sqrt(4-x^2))
What is the first derivative of arccos(x/2) ?
The first derivative of arccos(x/2) is -1/(sqrt(4-x^2))