Let f(x)= e^x g(x) with f(ln(2))=4, f'(ln(2))=6, , then g'(ln(2))=

Question

Let f(x)= e^x g(x)

 with f(ln(2))=4, f'(ln(2))=6,

, then g'(ln(2))= 

 

Answer 1

f(x) = e^xg(x)

f(ln2) = e^ln2g(ln2) = 2g(ln2) = 4. So, g(ln2) = 2

f'(x) = e^xg(x) + e^xg'(x)

f'(ln2) = 2g(ln2) + 2g'(ln2) = 4 + 2g'(ln2) = 6. So, g'(ln2) = 1.