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If f(x)=|(log)e x| , then (a) f'(1^+)=...

If `f(x)=|(log)_e x|` , then (a) `f'(1^+)=1` (b) `f^'(1^(-))=-1` (c) `f'(1)=1` (d) `f'(1)=-1`

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To solve the problem, we need to analyze the function \( f(x) = |\log_e x| \) and determine its derivatives at the point \( x = 1 \) from both the left and the right. ### Step 1: Understanding the Function The function \( f(x) = |\log_e x| \) takes the logarithm of \( x \) and applies the absolute value. The logarithm function, \( \log_e x \), is defined for \( x > 0 \) and has the following properties: - \( \log_e 1 = 0 \) - \( \log_e x < 0 \) for \( 0 < x < 1 \) - \( \log_e x > 0 \) for \( x > 1 \) ...
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RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
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  5. If f(x)=|(log)e x| , then (a) f'(1^+)=1 (b) f^'(1^(-))=-1 (c) f'...

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  6. If f(x)=|(log)e|x| , then f(x) is continuous and differentiable for...

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  18. If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)c...

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