What is the tangent of f(x)=2xe^xcos(x),\at x=0 ?

The tangent of f(x)=2xe^xcos(x),\at x=0 is y=2x

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tangent of f(x)=2xe^xcos(x),\at x=0

tangent of

f (x) = 2 x e^{x} cos (x), at x = 0

y = 2 x

Solution steps

Find the tangent point:

(0, 0)

Find the slope of

f (x) = 2 x e^{x} cos (x) : \frac{df ( x )}{d x} = 2 (e^{x} cos (x) + x (e^{x} cos (x) - e^{x} sin (x)))

Compute the slope of

f (x) = 2 x e^{x} cos (x)

x = 0 : m = 2

Find the line with slope m=

2

and passing through

(0, 0) : y = 2 x

y = 2 x

\int_{0}^{2} sin (x) + e^{x} d x

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

s^{2} - 4 s + 3

\int (x^{4} - 1) x^{2} d x

\frac{d y}{d x} = y (2 - 3 y)

What is the tangent of f(x)=2xe^xcos(x),\at x=0 ?
The tangent of f(x)=2xe^xcos(x),\at x=0 is y=2x