How do you differentiate f(x)= 5sinx*(1-2x)(x+1)-3f(x)=5sinx(12x)(x+1)3 using the product rule?

1 Answer
May 13, 2017

f'(x) =-20xsin(x) -5sin(x)-10x^2cos(x)-5xcos(x)+5cos(x)

Explanation:

Product Rule:
[f(x)g(x)]'=f'(x) g(x)+f(x)g'(x)
Set f(x)=5sin(x) and g(x)=(1-2x)(x+1)

(1)
d/dx[5sin(x)]=5cos(x)

(2)
d/dx[(1-2x)(x+1)]=d/dx[-2x^2-x+1]=-4x-1

Putting it all together
f'(x) =d/dx[5sin(x)(1-2x)(x+1)]-d/dx[3]
f'(x) =(5sin(x)(-4x-1))+5cos(x)(-2x^2-x+1)-0
f'(x) =-20xsin(x) -5sin(x)-10x^2cos(x)-5xcos(x)+5cos(x)