What is the Derivative of lnx^2 [Solved]

The derivative of lnx^2 is equal to 2/x. The natural logarithm of x² is denoted by ln(x²), and its derivative formula is given by

$\dfrac{d}{dx}(\ln x^2)=\dfrac{2}{x}.$

That is, the differentiation of ln(x²) is 2/x.

Derivative of ln(x²) by Chain Rule

Answer: The derivative of ln(x2) is 2/x.

Explanation:

To find the derivative of ln(x²) by the chain rule, let us put

z = x².

So $\dfrac{dz}{dx}$ = 2x.

Now,

$\dfrac{d}{dx}(\ln x^2)$ = $\dfrac{d}{dz}(\ln z) \times \dfrac{dz}{dx}$

= $\dfrac{1}{z} \times 2x$

= $\dfrac{2x}{z}$

= $\dfrac{2x}{x^2}$ as z=x².

= $\dfrac{2}{x}$.

So the derivative of ln(x²) is equal to 2/x, and this is obtained by the chain rule of differentiation.

More Derivatives:

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