If $$f(x)$$ is the primitive ofsin⁡$$x3log$$⁡(1+3x)$$tan$$−$$1$$⁡$$x2ex3$$−$$1(x$$≠$$0)$$ then limx→$$0$$ f′(x) is

Correct option is 4none of these

Questions

If $f (x)$ is the primitive of
$\frac{\sin \sqrt[3]{x} \log (1 + 3 x)}{{(\tan^{- 1} \sqrt{x})}^{2} (e^{\sqrt[3]{x}} - 1)} (x \neq 0) then lim_{x \to 0} f^{'} (x)$ is

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detailed solution

Correct option is D

limx→0 f′(x)=limx→0 sin⁡x3log⁡(1+3x)tan−1⁡x2ex3−1\=limx→0 3sin⁡x3x3×log⁡(1+3x)3x×xtan−1⁡x2x3ex3−1=3(1)(1)(1)2(1)=3

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If f(x) is the primitive ofsin⁡x3log⁡(1+3x)tan−1⁡x2ex3−1(x≠0) then limx→0 f′(x) is

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Ready to Test Your Skills?

free study material

If $f (x)$ is the primitive of
$\frac{\sin \sqrt[3]{x} \log (1 + 3 x)}{{(\tan^{- 1} \sqrt{x})}^{2} (e^{\sqrt[3]{x}} - 1)} (x \neq 0) then lim_{x \to 0} f^{'} (x)$ is