SOLUTION: if f(x) = 4(sqrt)xln(x) find f'(x) and then f'(2)=?

Algebra ->  Functions -> SOLUTION: if f(x) = 4(sqrt)xln(x) find f'(x) and then f'(2)=?       Log On


   

Question 1160035: if f(x) = 4(sqrt)xln(x) find f'(x) and then f'(2)=?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
if f%28x%29+=+4sqrt%28x%29ln%28x%29 find f'%28x%29 and then f'%282%29=?

f'%28x%29+=%28d%2Fdx%29%28+4sqrt%28x%29ln%28x%29%29........take constant out
f'%28x%29+=4%28d%2Fdx%29%28sqrt%28x%29%2A+ln%28x%29%29
apply the Product Rule: %28f%2Ag%29'=f'*g+f* g'

+f'

%28d%2Fdx%29sqrt%28x%29=1%2F%282sqrt%28x%29%29
%28d%2Fdx%29ln%28x%29=1%2Fx

f'%28x%29+=4%28ln%28x%29%2F%282sqrt%28x%29%29%2Bsqrt%28x%29%2Fx%29

f'

f'%28x%29+=4%28ln%28x%29%2F%282sqrt%28x%29%29%2Bx%2F%28x%2Asqrt%28x%29%29%29

f'%28x%29+=4%28ln%28x%29%2F%282sqrt%28x%29%29%2B2%2F%282sqrt%28x%29%29%29
f'%28x%29+=2%28ln%28x%29%2F%28sqrt%28x%29%29%2B2%2F%28sqrt%28x%29%29%29
f'%28x%29+=%282%28ln%28x%29%2B2%29%29%2Fsqrt%28x%29

then
f'%282%29=%282%28ln%282%29%2B2%29%29%2Fsqrt%282%29
f'%282%29=3.808685