SOLUTION: find the derivative of the function y = 2^3^x^2

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Question 353583: find the derivative of the function
y = 2^3^x^2
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+2%5E%283%5E%28x%5E2%29%29
Use the chain rule,
Let u=3%5E%28x%5E2%29, let v=x%5E2,
dy%2Fdx=%28dy%2Fdu%29%2A%28du%2Fdx%29
du%2Fdx=%28du%2Fdv%29%2A%28dv%2Fdx%29
dy%2Fdx=%28dy%2Fdu%29%2A%28du%2Fdv%29%2A%28dv%2Fdx%29
dy%2Fdu=2%5Eu%2Aln%282%29
du%2Fdv=3%5Ev%2Aln%283%29
dv%2Fdx=2x
Putting it all together,
dy%2Fdx=2%5E%28u%29%2Alog%282%29%2A3%5E%28v%29%2Aln%283%29%2A2x
dy%2Fdx=ln%282%29%2Aln%283%29%2A2%5E%28u%2B1%29%2A3%5E%28v%29%2Ax
dy%2Fdx=ln%282%29%2Aln%283%29%2A2%5E%283%5E%28x%5E2%29%2B1%29%2A3%5E%28x%5E2%29%2Ax