Let with . Which of the following equals…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

I(x,a)=\displaystyle \int \frac{dx}{x^{2}+a^{2}}

with

a\neq 0

. Which of the following equals

\displaystyle \frac{\partial I}{\partial a}

? (a)

-\dfrac{1}{a^{2}}\tan^{-1}\!\left(\dfrac{x}{a}\right)+\dfrac{x}{a(x^{2}+a^{2})}

(b)

\dfrac{1}{a^{2}}\tan^{-1}\!\left(\dfrac{x}{a}\right)-\dfrac{x}{a(x^{2}+a^{2})}

(c)

-\dfrac{1}{a^{2}}\tan^{-1}\!\left(\dfrac{x}{a}\right)-\dfrac{x}{a(x^{2}+a^{2})}

(d)

-\dfrac{1}{a^{2}}\tan^{-1}\!\left(\dfrac{x}{a}\right)

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