SOLUTION: (a) Let f(x)= sqrt(9+6x^2) Find f ' (x) (b) Let f(x)= e^sqrt(9+6x^2) Find f ' (x)

Algebra ->  Finance -> SOLUTION: (a) Let f(x)= sqrt(9+6x^2) Find f ' (x) (b) Let f(x)= e^sqrt(9+6x^2) Find f ' (x)       Log On


   

Question 1160095: (a) Let f(x)= sqrt(9+6x^2) Find f ' (x)
(b) Let f(x)= e^sqrt(9+6x^2) Find f ' (x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

(a)
Let f%28x%29=+sqrt%289%2B6x%5E2%29
Find f ' %28x%29:

apply the chain rule:%28df%2Au%29%2F%28dx%29=%28df%2Fdu%29%28du%2Fdx%29
f=sqrt%28u%29, u=9%2B6x%5E2

f'%28x%29=%28d%2Fdu%29%28u%29+%2A%28d%2Fdx%29%289%2B6x%5E2%29

%28d%2Fdu%29%28u%29=1%2F%282sqrt%28u%29%29
%28d%2Fdx%29%289%2B6x%5E2%29=12x


f'%28x%29=%281%2F%282sqrt%28u%29%29%29%2A12x

substitute back u=9%2B6x%5E2
f+' %28x%29=%281%2F%282sqrt%289%2B6x%5E2%29%29%29%2A12x

f'%28x%29=12x%2F%282sqrt%289%2B6x%5E2%29%29

f'%28x%29=6x%2F%28sqrt%289%2B6x%5E2%29%29


(b)
Let f%28x%29=+e%5Esqrt%289%2B6x%5E2%29+
Find f'%28x%29

apply the chain rule:%28df%2Au%29%2F%28dx%29=%28df%2Fdu%29%28du%2Fdx%29
f=e%5Eu, u=sqrt%289%2B6x%5E2%29

f'%28x%29=%28d%2Fdu%29%28e%5Eu%29+%2A%28d%2Fdx%29%28sqrt%289%2B6x%5E2%29%29

%28d%2Fdu%29%28e%5Eu%29+=e%5Eu
%28d%2Fdx%29%28sqrt%289%2B6x%5E2%29%29=6x%2Fsqrt%289%2B6x%5E2%29

f' %28x%29=e%5Eu%2A%286x%2Fsqrt%289%2B6x%5E2%29%29..........substitute back u=sqrt%289%2B6x%5E2%29

f'
f'