Differention using combination of rules help?

subzero12

while im on here i may as well ask cause
ive 4 problems using a combination of rules but there really confusing me
thanks in advance again for any help given

problem 1
sin2x/x^2+3x-2

problem 2
(3sinx)(x^3+2x+1)^6

problem 3
ln(4x^2+2x-1)^3

problem 4
tan3x^2(ln(2x-3))^3

Michael Collins

Should there be brackets in the first one?

Well taking is as you've written it you use the quotient rule and the chain rule on the first term, and just the usual differentiation rules on the remaining two terms.

The quotient rules says:

y(x) = u(x)/v(x)

y'(x) = [v(x) * u'(x) - u(x) * v'(x)]/ [v(x)]^2

where the dash (') means differentiation.

For example take

y(x) = 3x^2/[4x+1]

y'(x) = [(4x+1)* 6x - 3x^2 * 4] / [4x]^2 = [12x^2 + 6x] /16x^2

so apply a similar process to the first one and see how you get on.

Delphi91

Michael Collins wrote: »

...For example take

y(x) = 3x^2/[4x+1]

y'(x) = [(4x+1)* 6x - 3x^2 * 4] / [4x]^2 = [12x^2 + 6x] /16x^2 ...

Methinks it should be over [4x+1]^2 rather than [4x]^2.

Michael Collins

Yep, thank you.