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

##### 1 Answer

Jan 29, 2017

#### Answer:

#### 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#