The derivative of log_{10} x with respect to | vedclass

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

Question

(B) Let $u = \log_{10} x = \frac{\ln x}{\ln 10}$ and $v = \log_x 10 = \frac{\ln 10}{\ln x}$.We need to find $\frac{du}{dv}$.Note that $v = \frac{(\ln

Vedclass · Accepted Answer

$-(\log_{10} x)^2$

Vedclass · Answer

(B) Let $u = \log_{10} x = \frac{\ln x}{\ln 10}$ and $v = \log_x 10 = \frac{\ln 10}{\ln x}$.We need to find $\frac{du}{dv}$.Note that $v = \frac{(\ln 10)^2}{\ln x} \cdot \frac{1}{\ln 10} = \frac{1}{u}$.Thus, $v = u^{-1}$.Then $\frac{dv}{du} = -u^{-2} = -\frac{1}{u^2}$.Therefore, $\frac{du}{dv} = \frac{1}{dv/du} = -u^2$.Since $u = \log_{10} x$, we have $\frac{du}{dv} = -(\log_{10} x)^2$.

The derivative of $\log_{10} x$ with respect to $\log_x 10$ is

Similar Questions

If $y = 3^{x^2}$,then $\frac{dy}{dx}$ is equal to

$\frac{d}{dx}(\log_5 x^2) = $ . . . . . .

If $y = e^{(1 + \log_e x)}$,then the value of $\frac{dy}{dx} = $

$\frac{d}{dx} \log \tan \left( \frac{\pi}{4} + \frac{x}{2} \right) = $

$\frac{d}{dx} \left[ \log \left\{ e^x \left( \frac{x - 2}{x + 2} \right)^{3/4} \right\} \right]$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module