If     $y=\ln\sqrt{2x+1}$  ,

(a)  

Given $y=e^{4x}\left(e^{2-14x}\right)$  , the value of  $\frac{d^2x}{dy^2}$  given  $x=\frac{1}{5}$  is (a)  

If $y=6\cos\left(\theta-\frac{5\pi}{6}\right)$  , what is in an empty bracket of  $\frac{dy}{d\theta}=\left(...\right)\sin\left(\theta-\frac{5\pi}{6}\right)$  ?

(a)  

If $y=6\cos\left(\theta-\frac{5\pi}{6}\right)$  , state the value of  $\frac{dy}{d\theta}$  when  $\theta=\pi$  .

(a)  

If  $y=2\ln\left(\frac{1}{2x}\right)$  , then the simplest form of first derivative is  $\frac{dy}{dx}=\frac{m}{x^n}$  . What is m?

(a)  

If  $y=2\ln\left(\frac{1}{2x}\right)$  , then the simplest form of first derivative is  $\frac{dy}{dx}=\frac{m}{x^n}$  . What is n ?

(a)  

Given $y=\left(e^x+1\right)^2$  , then  $\frac{dy}{dx}=2e^a+be^x$  .
State the value of $b$ .

(a)  

Given $y=\left(e^x+1\right)^2$  , find  $\frac{dy}{dx}$  when  $x=\ln2$  .

(a)  

Find the simplest form of  $\frac{dy}{dx}$  if  $y=\sin^24x$ . 

(a)