Question

Which differentiation rules would you use to find the second derivative of f(x)= (3x^2 + 2x^2)^5

A) Chain Rule, Power Rule, Product Rule, Sum Rule
B) Chain Rule, Power rule, Sum rule
C) Chain Rule, Power rule, Quotient Rule, Sum rule
D) Power Rule, Product Rule, Sum Rule


I think is D but I am not sure

Answer 1

\[f(x)=(3x ^{3} +2x ^{2})^{5}\]

Answer 2

why not chain rule?
You have a function inside of a function

Answer 3

@freckles \[5(3x ^{3} +2x ^{2})^{4}\]
will that be the first derivative?

Answer 4

well you need to also find the derivative of the inside

Answer 5

\[\text{ first derivative } =5(3x^3+2x^2)^4 \cdot (3x^3+2x^2)'\]

Answer 6

you need to find the derivative of that sum inside the ( )'

Answer 7

so that will be \[9x ^{2}+4x\]

Answer 8

So \[\text{ first derivative } =5(3x^3+2x^2)^4 \cdot (9x^2+4x)\]

Answer 9

what rules were used to find the first derivative?

Answer 10

power rule, then product

Answer 11

what about chain rule?

Answer 12

whenever you take the derivative of the outside multiplied by derivative of inside
you are using chain rule

Answer 13

Also you can say we used product rule if you want to because you could use product rule to differentiate 9x^2

but you actually used sum rule since you found the derivative of a sum

Answer 14

D would be correct if it had one more rule in it

Answer 15

so A will be the correct answer as the first step was the chain rule, then power rule, then product rule and finished with the sum rule

Answer 16

Choice A sounds good

Answer 17

thank you for your help, i will practice more so i can understand more how to process with problem like this