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Popular >

derivative of arctan((1-2x/2))

Solution

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

Solution

- \frac{4}{4 x ^{2} - 4 x + 5}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( \frac{1 - 2 x}{2} ) ^{2} + 1} (- 1) : - \frac{4}{4 x ^{2} - 4 x + 5}

= - \frac{4}{4 x ^{2} - 4 x + 5}

Graph

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

taylor x/(1+x),1 taylor

\frac{x}{1 + x}, 1

integral from 0 to 9/2 of sqrt(81-x^2)

\int_{0}^{\frac{9}{2}} 81 - x^{2} d x

(dx)/(dt)=0.6-(3x)/(500)

\frac{d x}{d t} = 0.6 - \frac{3 x}{500}

(dy)/(dx)=8x(y-3)

\frac{d y}{d x} = 8 x (y - 3)

Frequently Asked Questions (FAQ)

What is the derivative of arctan((1-2x/2)) ?
The derivative of arctan((1-2x/2)) is -4/(4x^2-4x+5)
What is the first derivative of arctan((1-2x/2)) ?
The first derivative of arctan((1-2x/2)) is -4/(4x^2-4x+5)