f(0)=7, f’(0)=1, f(1)=8, f’(1)=8, g(1)=2, g’(1)=-9 and H(x)=f(ln(x))+ln(g(x)). Find dH/dx|x=1

Answer 1

f(0) = 7

f’(0) = 1

f(1) = 8

f’(1) = 8

g(1) = 2

g’(1) = -9

H(x) = f(ln(x)) + ln(g(x))

H'(x) = f'(ln(x)) * (1 / x) + (1 / g(x)) * g'(x) = (f'(ln(x) / x) + (g'(x) / g(x))

Find dH/dx at x = 1:

H'(1) = (f'(ln(1)) / 1) + (g'(1) / g(1)) = f'(0) + (g'(1) / g(1)) = 1 + (-9 / 2) = -7 / 2

Joanne,

I noticed that you've asked for help on many questions for the same topic. Please let me know if you'd like to set up a lesson to go over the material.

Thanks,

Janelle