Question

derivative: y=3^(xlnx)

Answer 1

know chain rule ?

Answer 2

somewhat

Answer 3

would it be 3^(xlnx) times d/dx (xlnx)

Answer 4

what is d/dx(a^x) ??

Answer 5

\(d/dx (a^{f(x)}) = (a^{f(x)})ln \:a\quad d/dx(f(x))\)

Answer 6

u just missed ln 3

Answer 7

so ln3^(xlnx) times d/dx (xlnx) ?

Answer 8

3^(xlnx) ln 3 times d/dx (xlnx)

Answer 9

is that some type of shortcut?

Answer 10

no, that is chain rule.

Answer 11

since d/dx of a^x = a^x ln a
from chain rule, we have
\(d/dx (a^{f(x)}) = (a^{f(x)})ln \:a\quad d/dx(f(x))\)

Answer 12

now just put here a=3, f(x) = x ln x

Answer 13

so then we just need to use the product rule for the right side correct

Answer 14

froduct rule for d/dx (x ln x)
yes, correct.

Answer 15

alryte got it thanks a lot hart

Answer 16

welcome ^_^