Product Rule Derivatives

Find the derivative.

 $f\left(x\right)=\left(3x^2-2x+6\right)\left(x^3+2x-3\right)$  

•  $f'\left(x\right)=15x^4-8x^3+36x^2-26x+18$  

•  $f'\left(x\right)=15x^4-9x^3+36x^2+15x-1$  

•  $f'\left(x\right)=3x^5-4x^2-18$  

•  $f'\left(x\right)=15x^4-6x^3+36x^2-2x+5$  

Find the equation of the line tangent to

 $f\left(x\right)=\left(3x^3-4x\right)\left(x^2+2x-1\right)$  at  $x=-2$  

•  $y-16=2\left(x+2\right)$  

•  $y=16$  

•  $y=-16$  

•  $y+16=2\left(x+2\right)$  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find the slope of the line tangent to the function at x=2

 $f\left(x\right)=\left(x^{-3}+2x\right)\left(4x+6\right)$  

•  $-\frac{107}{4}$  

•  $-\frac{335}{8}$  
  

•  $\frac{335}{8}$  

•  $-\frac{127}{8}$  

 $y=\left(x^2+4\right)\left(x^5-3x\right)$  at  $x=1$  

Find the equation of the line tangent to

•  $y-10=-6\left(x+1\right)$  

•  $y+10=-6\left(x-1\right)$  

•  $y-10=6\left(x-1\right)$  

•  $y+10=6\left(x-1\right)$  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.7

 $x=2$  

Find the slope of the line tangent to the function at the given x value.

 $f\left(x\right)=\left(\frac{2}{x^2}+4x\right)\left(\frac{3}{x}-2\right)$  

•  $-2$  

•  $-\frac{65}{8}$  

•  $\frac{61}{4}$  

•  $\frac{63}{8}$