Product Rule Derivatives

Find the derivative with respect to x.

 $y=2x^5\left(-x^5+4\right)$  

•  $\frac{dy}{dx}=2x^3\cdot-5x^4+\left(-x^5+4\right)\cdot6x^2\ =\ -16x^7+24x^2$  

•  $\frac{dy}{dx}=-x^5-5x^4+4$  

•  $\frac{dy}{dx}=2x^3\left(-x^5+4\right)+6x^{2\cdot}-5x^4=-2x^8-30x^6+8x^3$  

•  $\frac{dy}{dx}=-10x^7$  

Differentiate the function with respect to x.

 $y=x^5\left(x^4+3\right)$  

•  $\frac{dy}{dx}=x^5\cdot4x^3+\left(x^4+3\right)\cdot5x^4=9x^8+15x^4$  

•  $\frac{dy}{dx}=\left(x^4+3\right)\cdot5x^4=5x^8+15x^4$  

•  $\frac{dy}{dx}=x^5+5x^4$  

•  $\frac{dy}{dx}=x^5\left(x^4+3\right)+5x^4\cdot4x^3=x^9+20x^7+3x^5$  

Differentiate the function with respect to x.

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

•  $\frac{dy}{dx}=\left(-2x^3+5\right)\left(5x^4-2\right)-6x^2\cdot20x^3$  

•  $\frac{dy}{dx}=\left(-2x^3+5\right)\cdot-6x^2+\left(5x^4-2\right)\cdot20x^3$  

•  $\frac{dy}{dx}=-2x^3-6x^2+5$  

•  $\frac{dy}{dx}=\left(-2x^3+5\right)\cdot20x^3+\left(5x^4-2\right)\cdot-6x^2$  

Differentiate the function with respect to x.

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

•  $\frac{dy}{dx}=\left(-3x^4-3\right)\left(x^2-1\right)-12x^3\cdot2x$  

•  $\frac{dy}{dx}=\left(-3x^4-3\right)\cdot2x+\left(x^2-1\right)\cdot-12x^3$  

•  $\frac{dy}{dx}=-3x^4-12x^3-3$  

•  $\frac{dy}{dx}=\left(-3x^4-3\right)\cdot2x$  

Differentiate the function with respect to x.

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

•  $\frac{dy}{dx}=4x^5+20x^4+5$  

•  $\frac{dy}{dx}=\left(4x^5+5\right)\left(5x^4+12x^3\right)+\left(x^5+3x^4+2\right)\cdot20x^4$  

•  $\frac{dy}{dx}=\left(4x^5+5\right)\left(5x^4+12x^3\right)$  

•  $\frac{dy}{dx}=\left(4x^5+5\right)\left(x^5+3x^4+2\right)+20x^4\left(5x^4+12x^3\right)$