Easy
Find the derivative of $f(x) = 3$ at $x = 0$ and at $x = 3$.
- A$0$
- B$1$
- C$3$
- D$x$
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If $f(x) = \begin{cases} x-5, & \text{for } x \leq 1 \\ 4x^2-9, & \text{for } 1 < x < 2 \\ 3x+4, & \text{for } x \geq 2 \end{cases}$,then $f^{\prime}(2^{+})$ is equal to:
If $f(2)=4$ and $f^{\prime}(2)=1$,then $\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}$ is equal to
Differentiate the function with respect to $x$: $\sin(x^{2}+5)$.
Easy
View SolutionThe derivative of $e^{ax} \cos bx$ with respect to $x$ is $re^{ax} \cos(bx + \alpha)$,where $\alpha = \tan^{-1}(\frac{b}{a})$. When $a > 0, b > 0$,the value of $r$ is:
DifficultKCET 2010
View SolutionSuppose $f(x)$ is differentiable at $x = 1$ and $\mathop {\lim }\limits_{h \to 0} \frac{1}{h}f(1 + h) = 5$,then $f'(1)$ equals
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