What is the tangent of 4xe^x ?

The tangent of 4xe^x is y=4(e^{a_{0}}+e^{a_{0}}a_{0})x-4a_{0}^2e^{a_{0}}

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tangent of 4xe^x

tangent of

4 x e^{x}

y = 4 (e^{a_{0}} + e^{a_{0}} a_{0}) x - 4 a_{0}^{2} e^{a_{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = 4 x e^{x}

x = a_{0} : m = 4 (e^{a_{0}} + e^{a_{0}} a_{0})

Find the line with slope m=

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

and passing through

(a_{0}, 4 a_{0} e^{a_{0}}) : y = 4 (e^{a_{0}} + e^{a_{0}} a_{0}) x - 4 a_{0}^{2} e^{a_{0}}

y = 4 (e^{a_{0}} + e^{a_{0}} a_{0}) x - 4 a_{0}^{2} e^{a_{0}}

\int sin (t^{3}) d t

f (x) = \frac{1 + x - 4 x}{x}

x \cdot sin (\frac{2}{x})

\int_{0}^{2} (y + 2 - y^{2}) d y

\frac{d}{d x} (\frac{x ^{2}}{3 + x})

What is the tangent of 4xe^x ?
The tangent of 4xe^x is y=4(e^{a_{0}}+e^{a_{0}}a_{0})x-4a_{0}^2e^{a_{0}}