Question

Question #10423

Answer 1

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)`