What is the tangent of f(x)=(ln(x))^6,\at x=4 ?

The tangent of f(x)=(ln(x))^6,\at x=4 is y=48ln^5(2)x+64ln^6(2)-192ln^5(2)

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tangent of f(x)=(ln(x))^6,\at x=4

tangent of

f (x) = (ln (x))^{6}, at x = 4

y = 48 ln^{5} (2) x + 64 ln^{6} (2) - 192 ln^{5} (2)

Solution steps

Find the tangent point:

(4, 64 ln^{6} (2))

Find the slope of

f (x) = (ln (x))^{6} : \frac{df ( x )}{d x} = \frac{6 ln ^{5} ( x )}{x}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 48 ln^{5} (2)

Find the line with slope m=

48 ln^{5} (2)

and passing through

(4, 64 ln^{6} (2)) : y = 48 ln^{5} (2) x + 64 ln^{6} (2) - 192 ln^{5} (2)

y = 48 ln^{5} (2) x + 64 ln^{6} (2) - 192 ln^{5} (2)

What is the tangent of f(x)=(ln(x))^6,\at x=4 ?
The tangent of f(x)=(ln(x))^6,\at x=4 is y=48ln^5(2)x+64ln^6(2)-192ln^5(2)