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Popular >

derivative of arccos(x/2)

Solution

derivative of

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

y^'=(2x+sec^2(x))/(2y),y(0)=-3

y^{^{'}} = \frac{2 x + sec ^{2} ( x )}{2 y}, y (0) = - 3

(\partial)/(\partial y)(sin(xy^2z^3))

\frac{\partial}{\partial y} (sin (x y^{2} z^{3}))

(\partial)/(\partial x)(6y^2+284x-12)

\frac{\partial}{\partial x} (6 y^{2} + 284 x - 12)

derivative of (-2x/((1+x^2)^2))

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

derivative of y=e^7 derivative of

y = e^{7}

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))