What is the tangent of y=4e^x ?

The tangent of y=4e^x is y=4e^{a_{0}}x+4e^{a_{0}}-4e^{a_{0}}a_{0}

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tangent of y=4e^x

tangent of

y = 4 e^{x}

y = 4 e^{a_{0}} x + 4 e^{a_{0}} - 4 e^{a_{0}} a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 4 e^{a_{0}})

Find the slope of

y = 4 e^{x} : \frac{d y}{d x} = 4 e^{x}

Compute the slope of

y = 4 e^{x}

x = a_{0} : m = 4 e^{a_{0}}

Find the line with slope m=

4 e^{a_{0}}

and passing through

(a_{0}, 4 e^{a_{0}}) : y = 4 e^{a_{0}} x + 4 e^{a_{0}} - 4 e^{a_{0}} a_{0}

y = 4 e^{a_{0}} x + 4 e^{a_{0}} - 4 e^{a_{0}} a_{0}

\frac{\partial}{\partial t} (t^{2})

x \to 0 lim (arctan (6 x))

x \to - 3 lim (5 - x)

\frac{d}{d y} (\frac{1}{x + y})

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

What is the tangent of y=4e^x ?
The tangent of y=4e^x is y=4e^{a_{0}}x+4e^{a_{0}}-4e^{a_{0}}a_{0}