Product Rule

Let g be a function such that  $g\left(4\right)=8\ and\ g'\left(4\right)=-3$ . Let h be the function  $h\left(x\right)=\sqrt{x}$  . Let H be a function defined as  $H\left(x\right)=g\left(x\right)\cdot h\left(x\right)$  . Find H'(4)

 $\frac{d}{dx}\left(e^x\sin x\right)$  

•  $e^x\left(\sin x-\cos x\right)$  

•  $-e^x\cos x$  

•  $e^x\cos x$  

•  $e^x\left(\sin x+\cos x\right)$  

Which of the following can you ONLY do product rule?

•  $\ln x+e^x-\cos x$  

•  $e^xx^{5\ }$  

•  $e^x+x^4$  

•  $\left(x+1\right)\left(x-4\right)$  

 $\lim_{h\rightarrow0}\ \frac{2\left(\cos x+h\right)-2\cos x}{h}$  

•  $-\sin x$  

•  $-2\sin x$  

•  $2\cos x$  

•  $2\sin x$  

 $f\left(x\right)=5x^2\left(x+47\right)$  . Find  $f''\left(x\right)$  

•  $30x-470$  

•  $30x+470$  

•  $15x^2+235$  

•  $15x^2+470x$