Difficult
Let $f: R \rightarrow R$ satisfy the equation $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in R$ and $f(x) \neq 0$ for any $x \in R$. If the function $f$ is differentiable at $x=0$ and $f'(0)=3$,then $\lim_{h \rightarrow 0} \frac{1}{h}(f(h)-1)$ is equal to ....... .
- A$3$
- B$6$
- C$5$
- D$4$
Explore More
Similar Questions
Find the derivative: $\frac{d}{dx} \left( \frac{\log x}{\sin x} \right)$
Easy
View SolutionLet $f(x)$ and $g(x)$ be differentiable functions on $R$. If $h(x) = f(g(f(x)))$,where $f(2) = 1$,$g(1) = 2$ and $f'(2) = g'(1) = 4$,then $h'(2)$ is equal to:
Evaluate: $\frac{d}{d x}\left(3 \cos \left(\frac{\pi}{6}+x^{\circ}\right)-4 \cos ^3\left(\frac{\pi}{6}+x^{\circ}\right)\right) = $ . . . . . .
If $y = \sin^{-1}\sqrt{1 - x} + \cos^{-1}\sqrt{x}$,then $\frac{dy}{dx} = $
Medium
View SolutionIf $y = \frac{e^{2x} + e^{-2x}}{e^{2x} - e^{-2x}}$,then $\frac{dy}{dx} = $
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo