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Differentiate 2e^x^4 log⁡x w.r.t x.(a) \(\frac{2e^{x^4} (4x^4 log⁡x+1)}{x^2}\)(b) \(\frac{e^{x^4} (4x^4 log⁡x+1)}{x}\)(c) \(\frac{2e^{x^4} (4x^4 log⁡x+1)}{x}\)(d) –\(\frac{2e^{x^4} (4x^4 log⁡x+1)}{x}\)This question was addressed to me in an interview.This is a very interesting question from Exponential and Logarithmic Functions in chapter Continuity and Differentiability of Mathematics – Class 12

Answer»

Correct choice is (c) \(\FRAC{2e^{x^4} (4x^4 log⁡x+1)}{x}\)

Easy explanation: CONSIDER y=2e^x^4 log⁡x

\(\frac{dy}{dx}\)=\(\frac{d}{dx}\) (2e^x^4 log⁡x)

Differentiating w.r.t x by using CHAIN rule, we GET

\(\frac{dy}{dx}\)=2(log⁡x \(\frac{d}{dx} (e^{x^4})+e^{x^4}\frac{d}{dx}\) (log⁡x))

\(\frac{dy}{dx}\)=\(2(log⁡x.e^{x^4}\frac{d}{dx} {x^4}+e^{x^4}.\frac{1}{x})\)

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

\(\frac{dy}{dx}\)=\(2e^{x^4} (4x^3 log⁡x+\frac{1}{x})\)

∴\(\frac{dy}{dx}=\frac{(2e^{x^4} (4x^4 log⁡x+1))}{x}\)


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