What is the tangent of 2e^{x-2} ?

The tangent of 2e^{x-2} is y=2e^{a_{0}-2}x+2e^{a_{0}-2}-2e^{a_{0}-2}a_{0}

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tangent of 2e^{x-2}

tangent of

2 e^{x - 2}

y = 2 e^{a_{0} - 2} x + 2 e^{a_{0} - 2} - 2 e^{a_{0} - 2} a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 e^{a_{0} - 2})

Find the slope of

y = 2 e^{x - 2} : \frac{d y}{d x} = 2 e^{x - 2}

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 e^{a_{0} - 2}

Find the line with slope m=

2 e^{a_{0} - 2}

and passing through

(a_{0}, 2 e^{a_{0} - 2}) : y = 2 e^{a_{0} - 2} x + 2 e^{a_{0} - 2} - 2 e^{a_{0} - 2} a_{0}

y = 2 e^{a_{0} - 2} x + 2 e^{a_{0} - 2} - 2 e^{a_{0} - 2} a_{0}

3 7 x^{6} + 8 x^{5}

sin (x) sin (y) + y^{^{'}} cos (y) = 0

\frac{d}{d x} (3 x^{2} - 6 x + 7)

\frac{x + 1}{x ^{2} + 1}

\frac{d}{d x} (x e^{x^{6}})

What is the tangent of 2e^{x-2} ?
The tangent of 2e^{x-2} is y=2e^{a_{0}-2}x+2e^{a_{0}-2}-2e^{a_{0}-2}a_{0}