How do you differentiate f(x)=(2+x )sqrt(2-3xf(x)=(2+x)23x using the product rule?

1 Answer
Oct 4, 2016

f'(x)=u'v+v'u

Explanation:

Let u=2+x and v=sqrt(2-3x)
then u'=1 and v'=-3 x 1/2(2-3x)^(-1/2)(chain rule)
Subbing into f'(x)=u'v+v'u,
f'(x)=1(sqrt(2-3x))+(-3/2)(2-3x)^(-1/2)(2+x)
Simplifying,
f'(x)=sqrt(2-3x)-(3(2+x))/(2sqrt(2-3x))