જો f(x)=log _eleft(e^{2 x}left(frac{3 x+5}{5- | vedclass

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

Question

(D) આપેલ છે,$f(x)=\log _e\left(e^{2 x}\left(\frac{3 x+5}{5-3 x}\right)^{\frac{2}{3}}\right)$ $\log(ab) = \log a + \log b$ ગુણધર્મનો ઉપયોગ કરતા: $f(x)=

Vedclass · Accepted Answer

$\frac{13}{4}$

Vedclass · Answer

(D) આપેલ છે,$f(x)=\log _e\left(e^{2 x}\left(\frac{3 x+5}{5-3 x}\right)^{\frac{2}{3}}\right)$ $\log(ab) = \log a + \log b$ ગુણધર્મનો ઉપયોગ કરતા: $f(x)=\log _e e^{2 x}+\log _e\left(\frac{3 x+5}{5-3 x}\right)^{\frac{2}{3}}$ $f(x)=2 x+\frac{2}{3} \log _e\left(\frac{3 x+5}{5-3 x}\right)$ $\log(\frac{a}{b}) = \log a - \log b$ નો ઉપયોગ કરતા: $f(x)=2 x+\frac{2}{3}\left(\log _e(3 x+5)-\log _e(5-3 x)\right)$ $x$ ની સાપેક્ષમાં વિકલન કરતા: $\frac{d f}{d x}=2+\frac{2}{3}\left(\frac{3}{3 x+5}-\frac{-3}{5-3 x}\right)$ $\frac{d f}{d x}=2+2\left(\frac{1}{3 x+5}+\frac{1}{5-3 x}\right)$ $x=1$ માટે: $\left(\frac{d f}{d x}\right)_{x=1}=2+2\left(\frac{1}{3(1)+5}+\frac{1}{5-3(1)}\right)$ $=2+2\left(\frac{1}{8}+\frac{1}{2}\right)=2+2\left(\frac{1+4}{8}\right)=2+2\left(\frac{5}{8}\right)=2+\frac{5}{4}=\frac{13}{4}$

જો $f(x)=\log _e\left(e^{2 x}\left(\frac{3 x+5}{5-3 x}\right)^{\frac{2}{3}}\right)$,$x \neq \frac{-5}{3}, \frac{5}{3}$ હોય,તો $x=1$ આગળ $\frac{d f}{d x}$ નું મૂલ્ય શોધો.

Similar Questions

જો $y = e^{m \sin^{-1} x}$ અને $(1 - x^2) (\frac{dy}{dx})^2 = A y^2$ હોય,તો $A = . . . . . .$

$\frac{d}{dx} \left\{ \log \left( \frac{e^x}{1 + e^x} \right) \right\} = $

જો $f(x) = \log_{x^2}(\log x)$ હોય,તો $x = e$ આગળ $f'(x)$ ની કિંમત શું થાય?

જો $y=\log _{10} x+\log _x 10+\log _x x+\log _{10} 10$ હોય,તો $\frac{d y}{d x}=$

જો $y = \log_{\sin x}(\tan x)$ હોય,તો $\left( \frac{dy}{dx} \right)_{\pi/4} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module