What is the tangent of f(x)=(ln(x))^4,\at x=2 ?

The tangent of f(x)=(ln(x))^4,\at x=2 is y=2ln^3(2)x+ln^4(2)-4ln^3(2)

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tangent of f(x)=(ln(x))^4,\at x=2

tangent of

f (x) = (ln (x))^{4}, at x = 2

y = 2 ln^{3} (2) x + ln^{4} (2) - 4 ln^{3} (2)

Solution steps

Find the tangent point:

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

Find the slope of

f (x) = (ln (x))^{4} : \frac{df ( x )}{d x} = \frac{4 ln ^{3} ( 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 = 2 ln^{3} (2)

Find the line with slope m=

2 ln^{3} (2)

and passing through

(2, ln^{4} (2)) : y = 2 ln^{3} (2) x + ln^{4} (2) - 4 ln^{3} (2)

y = 2 ln^{3} (2) x + ln^{4} (2) - 4 ln^{3} (2)

y = \frac{x ^{3}}{5 - x ^{2}}

\frac{\partial}{\partial x} (ln (x^{2} + y^{4}))

y = 2 x^{2} + 5 x + 6, (- 2, 0)

\frac{d}{d x} (\frac{1}{2} x^{2} - \frac{1}{4} x + \frac{1}{3})

\int 4 \frac{cos ( x )}{sin ^{2} ( x )} d x

What is the tangent of f(x)=(ln(x))^4,\at x=2 ?
The tangent of f(x)=(ln(x))^4,\at x=2 is y=2ln^3(2)x+ln^4(2)-4ln^3(2)