What is the tangent of y=13xe^x ?

The tangent of y=13xe^x is y=13(e^{a_{0}}+e^{a_{0}}a_{0})x-13a_{0}^2e^{a_{0}}

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tangent of y=13xe^x

tangent of

y = 13 x e^{x}

y = 13 (e^{a_{0}} + e^{a_{0}} a_{0}) x - 13 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}, 13 a_{0} e^{a_{0}})

Find the slope of

y = 13 x e^{x} : \frac{d y}{d x} = 13 (e^{x} + e^{x} 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 = 13 (e^{a_{0}} + e^{a_{0}} a_{0})

Find the line with slope m=

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

and passing through

(a_{0}, 13 a_{0} e^{a_{0}}) : y = 13 (e^{a_{0}} + e^{a_{0}} a_{0}) x - 13 a_{0}^{2} e^{a_{0}}

y = 13 (e^{a_{0}} + e^{a_{0}} a_{0}) x - 13 a_{0}^{2} e^{a_{0}}

\frac{d y}{d x} - \frac{2 x ^{3} y}{x ^{4} + 3} = x^{3}

\frac{d}{d x} (2 A x + B)

\frac{d}{d x} (x^{6} ln (5 x))

\frac{d}{d x} (\frac{1}{x ^{2} + 2 y ^{2} - 5})

f (x) = 5 x + 6 x

What is the tangent of y=13xe^x ?
The tangent of y=13xe^x is y=13(e^{a_{0}}+e^{a_{0}}a_{0})x-13a_{0}^2e^{a_{0}}