Question

Differentiate log⁡(e^5x^3) w.r.t x.

(a) $\frac{-15x^2}{e^{5x^3}}$

(b) $\frac{15x^2}{e^{5x^3}}$

(c) 15x^2

(d) -15x^2

I got this question at a job interview.

The above asked question is from Exponential and Logarithmic Functions topic in chapter Continuity and Differentiability of Mathematics – Class 12

Answer 1

Correct answer is (c) 15x^2

The best I can explain: Consider y=log⁡(e^5x^3)

y=5x^3 (∴log⁡e^x=x)

⇒$\frac{dy}{dx}$=$\frac{d}{dx} (5x^3)$

∴$\frac{dy}{dx}=5(3x^2)=15x^2$