Question

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

Answer 1

Hello,

Step-by-step explanation:

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

$(ln(u)') = \frac{u'}{u}$

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

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

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

$y = \frac{12ln(x)}{x} (x - 10) + 4ln(10)$

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