Question

What is the value of \(\frac{d}{dx}\) (sin⁡ x tan⁡ x)?

(a) sin⁡ x + tan⁡ x sec⁡ x

(b) cos⁡ x + tan⁡ x sec⁡ x

(c) sin⁡ x + tan⁡ x

(d) sin⁡ x + tan⁡ x sec^2⁡x

I got this question in an interview for internship.

Question is taken from Derivatives topic in chapter Limits and Derivatives of Mathematics – Class 11

Answer 1

Correct option is (a) sin⁡ x + tan⁡ x sec⁡ x

Easy explanation: We follow product rule \(\frac{d}{dx}\) (f.g) = g.\(\frac{d}{dx}\) (f) + f.\(\frac{d}{dx}\) (g)   

Here, f = sin⁡ x and g = tan⁡ x

\(\frac{d}{dx}\) (sin⁡ x tan⁡ x) = cos⁡ x tan⁡ x + sec^2⁡ x sinx

\(\frac{d}{dx}\) (sin⁡ x tan⁡ x) = sin⁡ x + tan⁡ x sec⁡ x