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derivative of arctan(sqrt(x/a))

Solution

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

Solution

\frac{a}{2 x ( x + a )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{a}{2 x ( x + a )}

Popular Examples

derivative of-1/2 e^{-x/2}

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

integral of (x^2-3x+11)/((x^2-4x+10)^2)

\int \frac{x ^{2} - 3 x + 11}{( x ^{2} - 4 x + 10 ) ^{2}} d x

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

f (x) = \frac{x ^{3}}{4 - x ^{2}}

integral of sqrt(1+u^2)

\int 1 + u^{2} d u

integral from 0 to 4 of x^3sqrt(x^2+16)

\int_{0}^{4} x^{3} x^{2} + 16 d x

Frequently Asked Questions (FAQ)

What is the derivative of arctan(sqrt(x/a)) ?
The derivative of arctan(sqrt(x/a)) is (sqrt(a))/(2sqrt(x)(x+a))
What is the first derivative of arctan(sqrt(x/a)) ?
The first derivative of arctan(sqrt(x/a)) is (sqrt(a))/(2sqrt(x)(x+a))