Question

Differentiate 7 log⁡(x^4.5e^x^3) w.r.t x.

(a) \(\frac{7(4+3x^3)}{x^2}\)

(b) \(\frac{7(4-3x^3)}{x}\)

(c) –\(\frac{7(4+3x^3)}{x}\)

(d) \(\frac{7(4+3x^3)}{x}\)

I had been asked this question in an online quiz.

Asked question is from Exponential and Logarithmic Functions in portion Continuity and Differentiability of Mathematics – Class 12

Answer 1

The correct choice is (d) \(\frac{7(4+3x^3)}{x}\)

The best explanation: Consider y=7 log⁡(x^4.5e^x^3)

y=\(7(log⁡x^4 +log⁡5e^{x^3})\)

y=\(7(4 log⁡x+log⁡5e^{x^3})\)

\(\frac{dy}{dx}=7(4 \frac{d}{dx} (log⁡x)+\frac{d}{dx} (log⁡5e^{x^3}))\)

\(\frac{dy}{dx}=7(\frac{4}{x}+\frac{1}{5e^{x^3}} \frac{d}{dx} (5e^{x^3}))\)

\(\frac{dy}{dx}=7(\frac{4}{x}+\frac{1}{5e^{x^3}}.5e^{x^3}.\frac{d}{dx} {x^3})\)

\(\frac{dy}{dx}=7(\frac{4}{x}+\frac{1}{5e^{x^3}}.5e^{x^3}.3x^2)\)

\(\frac{dy}{dx}=7(\frac{4}{x}+3x^2)\)

∴\(\frac{dy}{dx}=\frac{7(4+3x^3)}{x}\)