Question

What is the value of \(\frac{d}{dx}\)(cos^2⁡ x  tan⁡ x) at x = 1?

(a) -1

(b) 0

(c) -2

(d) 1

The question was posed to me during an interview.

My doubt is from Derivatives in portion Limits and Derivatives of Mathematics – Class 11

Answer 1

Right option is (d) 1

For explanation I would say: We need to use product rule in both the terms to get the answer.

\(\frac{d}{dx}\) (f.g) = g.\(\frac{d}{dx}\) (f) + f.\(\frac{d}{dx}\) (g)

Here f = cos^2⁡ x and g = tan ⁡x

To differentiate f, we need to use chain rule.

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

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

At x = 1 we get,

= tan⁡0.(-2 cos⁡ 0 sin⁡ 0) + cos^2⁡ 0.sec^2 ⁡0

= 1