What is the tangent of e^{x+1} ?

The tangent of e^{x+1} is y=e^{a_{0}+1}x+e^{a_{0}+1}-e^{a_{0}+1}a_{0}

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tangent of e^{x+1}

tangent of

e^{x + 1}

y = e^{a_{0} + 1} x + e^{a_{0} + 1} - e^{a_{0} + 1} a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, e^{a_{0} + 1})

Find the slope of

y = e^{x + 1} : \frac{d y}{d x} = e^{x + 1}

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} + 1}

Find the line with slope m=

e^{a_{0} + 1}

and passing through

(a_{0}, e^{a_{0} + 1}) : y = e^{a_{0} + 1} x + e^{a_{0} + 1} - e^{a_{0} + 1} a_{0}

y = e^{a_{0} + 1} x + e^{a_{0} + 1} - e^{a_{0} + 1} a_{0}

- y^{^{'}} + \frac{2 y}{x} = \frac{y ^{2}}{x}

x \to \infty lim (ln (3 x) - ln (x + 7))

\frac{d y}{d t} = 2 y + 3 e^{2 t}

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

x \to 0 lim (\frac{( 9 ^{x} - 7 ^{x} )}{x})

What is the tangent of e^{x+1} ?
The tangent of e^{x+1} is y=e^{a_{0}+1}x+e^{a_{0}+1}-e^{a_{0}+1}a_{0}