Question

find the derivative
(a) y=x^2f(x)
(b) y=f(x)/x^2
(c) y= x^2/f(x)
(d) y=(1+xf(x))/sqrtx

Answer 1

f(x) is differentiable

Answer 2

i will do the first one, the rest are similar
by the product rule \((gf)'=g'f+f'g\) in our case \(g(x)=x^2, g'(x)=2x\) and \[f(x)=f(x), f'(x)=f'(x)\] is the best you can do, since you don't have an explicit description of \(f\) therefore the derivative of
\[x^2f(x)\] is
\[2xf(x)+x^2f'(x)\] by the product rule

Answer 3

the rest require the quotient rule, but the method is the same

Answer 4

is there any other way. the professor said to refrain from using the quotient rule if we could

Answer 5

your professor is mistaken
don't be scared of the quotient rule

Answer 6

ok

Answer 7

thank you

Answer 8

yw

Answer 9

whats the quotient rule again

Answer 10

@satellite73

Answer 11

never mind i got it