Question

Find the equation of the line tangent to the graph of f(x)=(lnx)^(4)at x=10

Answer 1

Hello,

Explanation:

`f(x) = ln(x) {}^(4)`

`(ln(u)') = (u')/(u)`

`f'(x) = \frac{4ln {}^{} (x) {}^(3) }{x}`

`f'(10) = \frac{4ln {}^{} (10) {}^(3) }{10} = (12ln(x))/(x)`

`f(10) = ln(10) {}^(4)`

`y = (12ln(x))/(x) (x - 10) + 4ln(10)`

`y = f'(a)(x - a) + f(a)`