Indian Navy AA (Artificer Apprentice) Differentiation — practice questions

Explore 2 free Differentiation questions in Indian Navy AA (Artificer Apprentice) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Differentiation with Quill →

Differentiation questions and exercises with answers

Showing questions 1–2 of 2.

$\dfrac{d}{dx}(\sin x)$ equals:Read the answer and worked solution →If $y = \tan^{-1}\left(\dfrac{2x}{1-x^2}\right)$, then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →

Worked practice questions

$\dfrac{d}{dx}(\sin x)$ equals:

$-\sin x$
$-\cos x$
$\cos x$
$\sec^2 x$

Show answer and solution

Correct answer: C. $\cos x$

Standard result: $d/dx(\sin x) = \cos x$.

Open this question →

If $y = \tan^{-1}\left(\dfrac{2x}{1-x^2}\right)$, then $\dfrac{dy}{dx}$ equals:

$\dfrac{2}{1+x^2}$
$\dfrac{-2}{1+x^2}$
$\dfrac{1}{\sqrt{1-x^2}}$
$\dfrac{1}{1+x^2}$

Show answer and solution

Correct answer: A. $\dfrac{2}{1+x^2}$

Recognise that $\tan^{-1}(2x/(1-x^2)) = 2\tan^{-1}x$ (double-angle identity, $|x| < 1$). So $dy/dx = 2/(1+x^2)$. Direct quotient-rule differentiation gives the same answer.