If y = log_{10}(x^2),then frac{dy}{dx} is equ | vedclass

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(B) Given $y = \log_{10}(x^2)$.Using the change of base formula $\log_a b = \frac{\log_e b}{\log_e a}$,we can rewrite the expression as:$y = \frac{\lo

Vedclass · Accepted Answer

$\frac{2}{x \log_e 10}$

Vedclass · Answer

(B) Given $y = \log_{10}(x^2)$.Using the change of base formula $\log_a b = \frac{\log_e b}{\log_e a}$,we can rewrite the expression as:$y = \frac{\log_e(x^2)}{\log_e 10}$Using the logarithmic property $\log(a^n) = n \log a$,we get:$y = \frac{2 \log_e x}{\log_e 10}$Differentiating both sides with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx} \left( \frac{2 \log_e x}{\log_e 10} \right)$Since $\frac{2}{\log_e 10}$ is a constant:$\frac{dy}{dx} = \frac{2}{\log_e 10} \cdot \frac{d}{dx}(\log_e x)$$\frac{dy}{dx} = \frac{2}{\log_e 10} \cdot \frac{1}{x} = \frac{2}{x \log_e 10}$.

If $y = \log_{10}(x^2)$,then $\frac{dy}{dx}$ is equal to

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