If f(x)=4sin(x)+3x^x, find f'(3).

Question

hartnn · Answer

that x^x is a tricky part
find its derivative separately
using logarithmic differentiation.
can you ?

anonymous · Answer

xln3x ?

hartnn · Answer

let me verify first
is it 
$3 (x^x)$
or 
$(3x)^x$
?

anonymous · Answer

x(1/3x)*3?

anonymous · Answer

it doesnt specify in the problem its just $$3x ^{x}$$

hartnn · Answer

ok, 
so let 
y = x^x
log y = log x^x = x log x 
try to differentiate 
log y = x log x using product rule on right and chain rule on left
what do u get ?

anonymous · Answer

It should differerentiate to 3(ln(x)+1)x^x +4cos(x)

anonymous · Answer

@hartnn i get x(1/x) so 1

hartnn · Answer

no, you didn't use product rule on right ?

anonymous · Answer

@BigTeach2345 i got that an i plugged in 3 and he answer i get is wrong):

anonymous · Answer

@hartnn ln(x)+1

hartnn · Answer

correct!
so
1/y y' = ln x +1 
so, y' = y (1+ ln x)
but y is x^x
so, derivative of x^x is x^x (1+ln x)
do you get this part ?

anonymous · Answer

yes

anonymous · Answer

Is your calculator in radians or degrees?

hartnn · Answer

so what about derivative of f(x) now ?
f(x)=4sin(x)+3x^x
f'(x) = ...?

anonymous · Answer

@gabyportillo95 I get 108.33 in radians and 116.284 in degrees

anonymous · Answer

its  3(ln(x)+1)x^x +4cos(x)

hartnn · Answer

thats correct, just plug in x=3 there

anonymous · Answer

i got it thank you! all i had to do was change it to radians :O

hartnn · Answer

i am glad you got it :)