1uniquebeauty 1uniquebeauty
  • 14-07-2022
  • Mathematics
contestada

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

Respuesta :

skabetix skabetix
  • 14-07-2022

Hello,

Step-by-step explanation:

[tex]f(x) = ln(x) {}^{4} [/tex]

[tex](ln(u)') = \frac{u'}{u} [/tex]

[tex]f'(x) = \frac{4ln {}^{} (x) {}^{3} }{x} [/tex]

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

[tex]f(10) = ln(10) {}^{4} [/tex]

[tex]y = \frac{12ln(x)}{x} (x - 10) + 4ln(10)[/tex]

[tex]y = f'(a)(x - a) + f(a)[/tex]

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