What is the tangent of y=e^{-9t} ?

The tangent of y=e^{-9t} is y=-9e^{-9a_{0}}t+e^{-9a_{0}}+9a_{0}e^{-9a_{0}}

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tangent of y=e^{-9t}

tangent of

y = e^{- 9 t}

y = - 9 e^{- 9 a_{0}} t + e^{- 9 a_{0}} + 9 a_{0} e^{- 9 a_{0}}

Solution steps

Compute the tangent line to the general point

t = a_{0}

Find the tangent point:

(a_{0}, e^{- 9 a_{0}})

Find the slope of

y = e^{- 9 t} : \frac{d y}{d t} = - 9 e^{- 9 t}

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 = - 9 e^{- 9 a_{0}}

Find the line with slope m=

- 9 e^{- 9 a_{0}}

and passing through

(a_{0}, e^{- 9 a_{0}}) : y = - 9 e^{- 9 a_{0}} t + e^{- 9 a_{0}} + 9 a_{0} e^{- 9 a_{0}}

y = - 9 e^{- 9 a_{0}} t + e^{- 9 a_{0}} + 9 a_{0} e^{- 9 a_{0}}

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What is the tangent of y=e^{-9t} ?
The tangent of y=e^{-9t} is y=-9e^{-9a_{0}}t+e^{-9a_{0}}+9a_{0}e^{-9a_{0}}