Question

What is the derivative of \(\frac{3x^2}{(1-sinx)}\)?

(a) \(\frac{6xsinx-3x^2 cosx}{(1-sinx)^2} \)

(b) \(\frac{6x}{1-sinx} \)

(c) \(\frac{6xsinx-3x^2 cosx-6x}{(1-sinx)^2} \)

(d) \(\frac{6xsinx-3cosx-6}{(1-sinx)^2} \)

This question was addressed to me in an internship interview.

My doubt is from Derivatives of Area in division Differential Calculus of Engineering Mathematics

Answer 1

Right option is (c) \(\frac{6xsinx-3x^2 cosx-6x}{(1-sinx)^2} \)

The best I can explain: Given: y =  \(\frac{3x^2}{(1-sinx)}\)

\(\frac{dy}{dx}=\frac{3x^2(\frac{d(1-sinx)}{dx})-(\frac{d(3x^2)}{dx})(1-sinx)}{(1-sinx)^2}\)

\(\frac{dy}{dx}=\frac{3x^2(-cosx)-6x(1-sinx)}{(1-sinx)^2}\)

\(\frac{dy}{dx}=\frac{6xsinx-3x^2 cosx-6x}{(1-sinx)^2}\)