# Calc

posted by Will

g'(x)=tan(2/1+x^2)

Let g be the function with first derivative given above and g(1)=5. If f is the function defined by f(x)=ln(g(x)), what is the value of f'(1)?

I know the answer is 0.311, but I need steps as to why. Please and thanks.

1. Damon

f = ln g
df/dx = df/dg * dg/dx
we were given dg/dx
what is df/dg ?
df/dg = d ln g / dg = 1/g

so df/dx = (1/g)tan 2/(1+x^2) I think you mean

= (1/5)tan 2/2 = (1/4) tan one radian or 180/pi deg
= (1/5)(1.055741 )
= .31148 so agree

## Similar Questions

1. ### inverse

If f(x)=cosx + 3 how do I find f inverse(1)?
2. ### solving trigonometrical equations

arctan(tan(2pi/3) thanks. arctan(tan(2pi/3) = -pi/3 since arctan and tan are inverse operations, the solution would be 2pi/3 the number of solutions to arctan(x) is infinite, look at its graph. generally, unless a general solution …
3. ### Calc

intergral of (x^3 -4x + 3)/(2x) dx would this be ln abs(x^3-4x+3) + C?
4. ### math-calc

for x (-12, 10) the function f is defined: f(x)=x^7(x+2)^2 On which two intervals is the function increasing (enter intervals in ascending order)?

Determine whether or not each of the following functions is invertible. Give your reasons for believing the function is invertible or not. Please check this for me. I am not sure if I am adequately explaining my answer and if my answer …
6. ### Calc

I'm creating a "calculu for dummies" project book. I've already done most of it, I'm just stuck on these ones. Thank you! -What is the definition of a derivative?