What is the tangent of e^x ?

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

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tangent of e^x

tangent

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = e^{x} : \frac{d y}{d x} = e^{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 = e^{a_{0}}

Find the line with slope m=

e^{a_{0}}

and passing through

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

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

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