Thread: Help with a question involving chain rule + product rule (derivative)

I'm having trouble finding the derivative of this function: x(3x - 9)^3

The answer is 27(x-3)^2 (4x - 3) but I don't know how to get there. It would be very much appreciated if anyone can provide a step-by-step solution to how they got to the answer. It doesn't have to be too detailed.

Thanks in advance.

Originally Posted by Archduke01

I'm having trouble finding the derivative of this function: x(3x - 9)^3

The answer is 27(x-3)^2 (4x - 3) but I don't know how to get there. It would be very much appreciated if anyone can provide a step-by-step solution to how they got to the answer. It doesn't have to be too detailed.

Thanks in advance.

Set f(x) = x and g(x) = (3x - 9)^3. First calculate f'(x) and g'(x) individually using the chain rule. Then use the product rule to get d/dx f(x)g(x) = f'(x)g(x) + f(x)g'(x), substituting in the values you found for all of these functions.

Originally Posted by Archduke01

I'm having trouble finding the derivative of this function: x(3x - 9)^3

The answer is 27(x-3)^2 (4x - 3) but I don't know how to get there. It would be very much appreciated if anyone can provide a step-by-step solution to how they got to the answer. It doesn't have to be too detailed.

Thanks in advance.

Tonio

Thanks so much for clarifying, guys. I appreciate it.

Originally Posted by tonio

Tonio

I don't understand that second line. Why is it ?

Originally Posted by Archduke01

I don't understand that second line. Why is it ?

Derivative of the first times the second plus the first times the derivative of the 2nd...the formula for derivative of a product! Of course, the second factor is composed, so you've to apply the chain rule ot it.

Tonio