- #1
FaraDazed
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Homework Statement
Find the derivative of [itex]4x^5(3x^2+3)^3 [/itex] by applying the chain rule twice.
Homework Equations
The Attempt at a Solution
I have had a go, but I have not used the chain rule twice so it probably will not be accepted even if it is mathmatically correct. But that is what I wanted to check, if the maths and thinking behind what I done is correct, as when I put it into a derivative calculator the answer is different.
What I did was break it down into two parts, using the chain rule to find the derivative of the second term (the one in paranatheses) and then applied the product rule.
I said...
If [itex]g=(3x^2+3)^3 [/itex] and [itex]h=3x^2+3 [/itex] and that [itex]c=h^3 [/itex]
Then, [itex]g'=h' \cdot c' = 6x \cdot 3(3x^2+3)^2 = 18x(3x^2+3)^2 [/itex]
Then if [itex] m=4x^5 [/itex] then [itex]y'=m' \cdot g + g' \cdot m [/itex]
[itex]y'=20x^4(3x^2+3)^3 + 18x(3x^2+3)^2 \\
y'=20x[x^3(3x^2+3)^3+\frac{9}{10}(3x^2+3)^2 ] [/itex]
Then I was not sure if doing this makes it look neater or even if its possible, as I am not too sure but if the above is correct then could I do...
[itex]20x(3x^2+3)^2[x(3x^2+3)+\frac{9}{10}] [/itex]
I would appreciate it if someone could check my maths and my method, and also to give advice on how to solve it by using the chain rule twice.
Thanks :)