Derivatives Review

Find the derivative of
 $f\left(x\right)=x^4\sin\left(x\right)$  

•  $x^4\cos\left(x\right)-4x^3\sin\left(x\right)$  
  

•  $x^4\cos\left(x\right)+4x^3\sin\left(x\right)$  
  

•  $4x^3\cos\left(x\right)$  

•  $-4x^3\cos\left(x\right)$  
  

Which of the following is the derivative of  $y=\left(3x^4-7\right)\left(5x^2+1\right)$  

•  $\left(12x^3\right)\left(10x\right)$  
  

•  $\left(3x^4-7\right)\left(10x\right)+\left(12x^3\right)\left(5x^2+1\right)$  
  

•  $\left(3x^4-7\right)\left(10x\right)-\left(12x^3\right)\left(5x^2+1\right)$  
  

•  $\frac{3x^4-7}{10x}+\frac{12x^3}{5x^2+1}$  
  

Find the derivative of 
 $f\left(x\right)=xe^x$  

•  $f'\left(x\right)=e^x$  

•  $f'\left(x\right)=2xe^x$  

•  $f'\left(x\right)=e^x-xe^x$  
  

•  $f'\left(x\right)=e^x+xe^x$  
  

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

• f'(x) = -24x^-4 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x
• f'(x) = 24x^-2 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x-1

Find  $\frac{\text{d}y}{\text{d}x}$  if  $y\ =\ 3x^5\cos x$  

•  $-15x^4\sin x$  

•  $15x^4\sin x$  

•  $15x^4\cos x-3x^5\sin x$  

•  $15x^4\cos x\ +\ 3x^5\sin x$  

 $y=\frac{2x^3-3x+1}{\sin x}$  , find y'.

•  $\frac{\left(\sin x\right)\left(6x^2-3\right)-\left(2x^3-3x+1\right)\left(\cos x\right)}{\sin^2x}$  

•  $\frac{\left(\sin x\right)\left(6x^2-3\right)-\left(2x^3-3x+1\right)\left(-\cos x\right)}{\sin^2x}$  

•  $\frac{\left(2x^3-3x+1\right)\left(\cos x\right)-\left(\sin x\right)\left(6x^2-3\right)}{\sin^2x}$  

•  $\frac{\left(2x^3-3x+1\right)\left(-\cos x\right)-\left(\sin x\right)\left(6x^2-3\right)}{\sin^2x}$  

 $f\left(x\right)=\left(3-\sqrt{x}\right)\left(2x^4-4x+1\right)$  , find f'(x)

•  $\left(-\frac{1}{2\sqrt{x}}\right)\left(8x^3-4\right)$  

•  $\left(3-\frac{1}{2\sqrt{x}}\right)\left(2x^4-4x+1\right)+\left(3-\sqrt{x}\right)\left(8x^3-4\right)$  

•  $\left(-\frac{1}{2\sqrt{x}}\right)\left(2x^4-4x+1\right)+\left(3-\sqrt{x}\right)\left(8x^3\right)$  

•  $\left(-\frac{1}{2\sqrt{x}}\right)\left(2x^4-4x+1\right)+\left(3-\sqrt{x}\right)\left(8x^3-4\right)$  

 $f\left(x\right)\ =\ e^x\sin x$  

•  $f'\left(x\right)\ =\ e^x\cos x$  

•  $f'\left(x\right)\ =\ e^x\cos x\ +\ \sin xe^x$  

•  $f'\left(x\right)\ =\ e^x\cos x\ +\ \sin x$  

•  $f'\left(x\right)\ =\ e^x\cos x\ -\ \sin xe^x$  

 $y\ =\ 10x^{3\ }+\sqrt{x^3}-4\sin x$  

•  $y'\ =\ 30x^2+\frac{3}{2}\sqrt{x}-4\cos x$  

•  $y'\ =\ 20x^3+\frac{2}{3}\sqrt{x}+4\cos x$  

•  $y'\ =\ 30x^3+x^{\frac{3}{2}}-4\cos x$  

•  $y'\ =\ 30x^{ }+\frac{3}{2}\sqrt{x}+\cos x$  

 $y\ =\ \left(9^x\right)\left(\frac{3}{x^2}\right)$  

•  $y'\ =\ \left(9^x\right)\left(\frac{-6}{x^3}\right)-\left(\frac{3}{x^2}\right)\left(9^x\right)\left(\ln9\right)$  

•  $y'\ =\ \left(9^x\right)\left(\frac{6}{x^{-3}}\right)+\left(\frac{3}{x^2}\right)\left(9^x\right)$  

•  $y'\ =\ \left(9^x\right)\left(\frac{-6}{x^3}\right)+\left(\frac{3}{x^2}\right)\left(9^x\right)\left(\ln9\right)$  

•  $y'\ =\ \left(9^x\right)\left(\frac{-6}{x^3}\right)-\left(\frac{3}{x^2}\right)\left(\ln9\right)$