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Popular >

derivative of f(x)=arctan(2/x)

Solution

derivative of

f (x) = arctan (\frac{2}{x})

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of x*cos(kx)

\int x \cdot cos (k x) d x

tangent of-10x^4+x^3 tangent of

- 10 x^{4} + x^{3}

derivative of y=x^{13/14}derivative of

y = x^{\frac{13}{14}}

sum from n=1 to infinity of ln((n+1)^2)

n = 1 \sum \infty ln ((n + 1)^{2})

2y^{''}+5y^'-3y=0,y(0)=1,y^'(0)=4

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 4

Frequently Asked Questions (FAQ)

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