Question

Can I use the product rule on the denominator to plug into the quotient rule to find t derivative?

Answer 1

Yes, you can use the product rule on the denominator to plug into the quotient rule to find the derivative.

Step-by-step explanation:

Yes, you can use the product rule on the denominator to plug into the quotient rule to find the derivative.

The product rule states that if you have two functions, f(x) and g(x), then the derivative of their product is given by (f'(x) * g(x)) + (f(x) * g'(x)).

Similarly, the quotient rule states that if you have two functions, f(x) and g(x), then the derivative of their quotient is given by (f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2.

Therefore, to find the derivative of a function that involves both product and quotient, you can apply the product rule to the denominator and then plug it into the quotient rule.

Answer 2

`(t^2)/((t-4)(2-t^3))^{}=t^2(t-4)^(-1)(2-t^3)^(-1)`
`z^(\prime)=2t(t-4)^(-1)(2-t^3)^(-1)+t^2(-1)(t-4)^(-2)(1)(2-t^3)^(-1)+t^2(t-4)^(-1)(-1)(2-t^3)^(-2)(-3t^2)`