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Popular >

derivative of arccos(((x+1)/2))

Solution

\frac{d}{d x} (arccos (\frac{( x + 1 )}{2}))

Solution

- \frac{1}{- x ^{2} - 2 x + 3}

Solution steps

\frac{d}{d x} (arccos (\frac{( x + 1 )}{2}))

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{- x ^{2} - 2 x + 3}

Graph

Popular Examples

integral from-7 to 0 of 1/(sqrt(9-x))

\int_{- 7}^{0} \frac{1}{9 - x} d x

derivative of (sqrt(x^5)/(x^3))

\frac{d}{d x} (\frac{x ^{5}}{x ^{3}})

derivative of 5x^2cos(x+x)

\frac{d}{d x} (5 x^{2} cos (x) + x)

(\partial)/(\partial y)(((y+x))/((y-x)))

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

tangent of f(x)=x^2-2 tangent of

f (x) = x^{2} - 2

Frequently Asked Questions (FAQ)

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