Homework Help: Solving derivative- possible without quotient rule?

1. Oct 28, 2013

Persimmon

1. The problem statement, all variables and given/known data
find the following derivative
d/dx [g(x + 1)(√(2+ (x + 8)^(1/3))/(cos(tan(sin(tan(sin x))))]
at x = 0

2. Relevant equations

3. The attempt at a solution

I split the big long derivative into 3 functions:
a(x) = g(x + 1)
b(x) = √(2+ (x + 8)^(1/3))
c(x) = cos(tan(sin(tan(sin x))))

and got : (a'x*bx + b'x*ax)(cx)-c'x*px*qx)/cx^2
subbing in x = 0 that simplified into 2*g'(1)
but it was mentioned that it's possible to solve this without the quotient rule. I can't figure out how you would solve this derivative if you didn't use the quotient rule.

2. Oct 28, 2013

Staff: Mentor

Instead of dividing by cos(...), you can multiply by sec(...). That way you're set up to use the product rule.

As written this looks like a' * x * b * x etc. To be clearer, write a'(x) * b(x) etc.

3. Oct 28, 2013

Persimmon

Sorry for the unclear notation. I was trying to make it clearer so there wouldn't be endless brackets but I guess it's even more confusing that way. Thank you for your help!