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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Similar Questions

If $y = \log_2(\log_2 x)$,then $\frac{dy}{dx}$ is equal to

If $y = \log \log x$,then $e^y \frac{dy}{dx} = $

The differential coefficient of $f[\log (x)]$ with respect to $x$ when $f(x) = \log x$ is:

If $y = e^{m \sin^{-1} x}$ and $(1 - x^2) (\frac{dy}{dx})^2 = A y^2$,then $A = . . . . . .$

If $y = \log \left(\frac{1-x^{2}}{1+x^{2}}\right)$,then $\frac{dy}{dx}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module