Question

How do you find the derivative of `y=(2x^3+4)(x^2-3x+1)`?

Answer 1

`dy/dx=10x^4-24x^3+6x^2+8x-12`

Explanation:

differentiate using the `color(blue)"product rule"`

`"Given "y=f(x).g(x)" then"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=f(x)g'(x)+g(x)f'(x))color(white)(2/2)|)))larr" product rule"`

`"here "f(x)=2x^3+4rArrf'(x)=6x^2`

`"and "g(x)=x^2-3x+1rArrg'(x)=2x-3`

`rArrdy/dx=(2x^3+4)(2x-3)+(x^2-3x+1).6x^2`

distributing brackets.

`=4x^4-6x^3+8x-12+6x^4-18x^3+6x^2`

`rArrdy/dx=10x^4-24x^3+6x^2+8x-12`