Question
Asked Nov 2, 2019

Logarithmic Differentiation of (ln x)^x^2

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Step 1

Given expression

(In x)
To find logarithmic differentiation of the given expression
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(In x) To find logarithmic differentiation of the given expression

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Step 2

In implicit differentiation, we differentiate each side of an equation by treating one of the variables as a function of the other. We treat y as an implicit function of x.

Note: i) We use the chain rule to differentiate composite function:
Iff and g are both differentiable and F = f'g (i.e. F(x)= f(g(x))) is the
composite function, then
F'(x) f(g(x)) g'(x)
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Note: i) We use the chain rule to differentiate composite function: Iff and g are both differentiable and F = f'g (i.e. F(x)= f(g(x))) is the composite function, then F'(x) f(g(x)) g'(x)

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Step 3

To begin with:...

Let y (Inx)*
Taking log on both sides,
In y In [In x)*]
x2ln[ln x
In y
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Let y (Inx)* Taking log on both sides, In y In [In x)*] x2ln[ln x In y

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Math

Calculus