What is the tangent of y=e^x ?

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

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tangent of y=e^x

tangent of

y = e^{x}

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}

Compute the slope of

y = e^{x}

x = a_{0} : 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}

x \cdot tan (x)

t \cdot cos (t)

\frac{d}{d x} (sinh^{3} (\frac{1}{x}))

\int (sin (x) - 6 cos (x)) d x

\int_{1}^{\infty} \frac{2}{x} d x

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