Limits and Deri...

lf $$[\mathrm{x}]$$ denotes the greatest integer contained in $$\mathrm{x},$$ then for 4 $$<\mathrm{x}<5,\ \displaystyle \frac{d}{dx}\{[x]\}=$$

If $$y=3  \cos x$$, then $$\dfrac{dy}{dx}$$ at $$x=\dfrac{\pi}{2}$$ is

lf $$f(x)=\left\{\begin{matrix}\displaystyle \frac{1-\cos x}{x} &x\neq 0 \\ 0 & x=0\end{matrix}\right.$$,  then $$f^{'}(0)=$$

If $$\displaystyle \lim_{x\to0}{\displaystyle \frac{x^n - \sin^nx}{x - \sin^nx}}$$ is non-zero finite, then $$n$$ must be equal

If $$y=x^{-\tfrac12}+\log_5x+\displaystyle \frac {\sin x}{\cos x}+2^x$$, then find $$\dfrac {dy}{dx}$$

If $$\displaystyle y=5^{3-x^2}+(3-x^2)^5$$, then $$\displaystyle \frac{dy}{dx}=$$

If $$y=\log_{3}x+3 \log_{e} x+2 \tan x$$, then $$\displaystyle \frac{dy}{dx}=$$

Find the derivative of $$\sec^{-1}\left (\displaystyle \frac {x+1}{x-1}\right )+\sin^{-1}\left (\displaystyle \frac {x-1}{x+1}\right )$$

If $$y=\log_{10}x+\log_x 10+\log_xx+\log_{10} 10$$, then $$\displaystyle \frac{dy}{dx}=$$

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