Question #10423

1 Answer
Dec 7, 2017

Use the product rule #(d/dx (fg) = (df)/dxg + (dg)/dxf)# and the chain rule (#d/dx (f(g(x))) = (dg)/dx*(df)/(dg) = (df)/dx#). Answer up in explanation

Explanation:

Using the product rule first...

#(df)/dx = e^(x^2)d/dx (4x^3+5) + (4x^3+5)d/dx(e^(x^2))#

Next. we perform the chain rule...

#(df)/dx= 12x^2e^(x^2) + 2x(4x^3+5)e^(x^2)`#
#(df)/dx= (8x^4+12x^2+10x)e^(x^2)#