Logarithmic differentiation is a method by which a complex function is simplified by taking logarithm before differentiating.

True

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False

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Solution

The correct option is A
True

This is true. Logarithmic differentiation is only a method to simplify the function for convenience before it is differentiated.

Some examples of functions that can be simplified for the sake of differentiation are given below,

1) $y = x^{e^{x}}$ upon taking log becomes $l n y = e^{x} . I n x .$

2) $y = 7 (c o s x)^{\frac{x}{2}}$ upon taking log becomes $l n y = l n 7 + \frac{x}{2} . l n (c o s x)$

3) $y = \frac{x^{2 x} . (x - 1)^{3}}{(3 + 5 x)^{4}}$ upon taking log becomes $l n y = 2 x . l n x + 3 l n (x - 1) - 4. l n (3 + 5 x)$

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