Question

How do you know whether to use chain, product or quotient rule?

Answer 1

Think about the order of operations. What's the last operation you would do if you had a number and were doing arithmetic.

`f(x)=5x^2 sinx`
Last operation is multiply. Use the product rule.

`g(x)= (4x^2+3)/(2x-1)`
Last operation is division, use the quotient rule.

`h(x)=(5x^2+1)^9`
Last operation is raise to the 9th power, but it's not just `x^9`, use the chain rule.

`F(x)=3x^5cos(7x-1)` Last operation is multiply, use the product rule, but, whe you take the derivative of `cos(7x-1)`, you'll need the chain rule.

`G(x)=((3x+2)/(x-5))^7`

Use the derivative of the 7th power and (because it's not simply `x^7`, you'll also need the chain rule and to find the derivative of `(3x+2)/(x-5)` (the "inside function")

If you rewrite `G(x)=(3x+2)^7/(x-5)^7`, then the last operation is division, so we'll need the quotient rule. (And the power and chain rules).