What is the tangent of x^6,\at x=3 ?

The tangent of x^6,\at x=3 is y=1458x-3645

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tangent of x^6,\at x=3

tangent of

x^{6}, at x = 3

y = 1458 x - 3645

Solution steps

Find the tangent point:

(3, 729)

Find the slope of

y = x^{6} : \frac{d y}{d x} = 6 x^{5}

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 = 1458

Find the line with slope m=

1458

and passing through

(3, 729) : y = 1458 x - 3645

y = 1458 x - 3645

x \to 0 lim (\frac{x}{x - 1})

\frac{d y}{d x} + y = e^{3 x}

\frac{d y}{d x} - y = 3 e^{8 x}

\frac{cos ( x )}{x ^{4}}

\frac{d}{d x} (5 x + 7)