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Grade 12Differential Calculus

Differential of log^n x

Profile image of milind
11 Years agoGrade 12
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1 Answer

Profile image of Jitender Singh
11 Years ago
Ans:
f(x) = log^{n}(x)
f'(x) = n.log^{n-x}(x).\frac{1}{x}
f'(x) = \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}
f'(x) = \lim_{h\rightarrow 0}\frac{(log(x+h))^{n}-(log(x))^{n}}{h}
It is a zero by zero form, so apply L’Hospital rule
f'(x) = \lim_{h\rightarrow 0}\frac{n(log(x+h))^{n-1}}{1}.\frac{1}{x+h}
f'(x) = n(log(x))^{n-1}.\frac{1}{x}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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