Question

Differentiate 5e^x^2 tan⁡x w.r.t x.

(a) 5e^x^2 (1+tan⁡x)^2

(b) -5e^x^2 (1+tan⁡x)^2

(c) 5e^x^2 (1-tan⁡x)^2

(d) -5e^x^2 (1-tan⁡x)^2

I had been asked this question in an interview for job.

My doubt is from Exponential and Logarithmic Functions topic in portion Continuity and Differentiability of Mathematics – Class 12

Answer 1

The correct answer is (a) 5e^x^2 (1+tan⁡x)^2

To explain I would say: Consider y=5e^x^2 tan⁡x

Differentiating w.r.t x by using chain rule, we get

\(\frac{dy}{dx}\)=tan⁡x \(\frac{d}{dx}\) (5e^x^2)+5e^x^2 \(\frac{d}{dx}\) (tan⁡x)

\(\frac{dy}{dx}\)=tan⁡x (5e^x^2.2x)+5e^x^2 (sec^2⁡x)

\(\frac{dy}{dx}\)=5e^x^2 (2x tan⁡x+sec^2⁡x)

\(\frac{dy}{dx}\)=5e^x^2 (1+tan^2⁡x+2x tan⁡x)

\(\frac{dy}{dx}\)=5e^x^2 (1+tan⁡x)^2