What is the tangent of f(x)=e^{4x}cos(pix),\at x=0 ?

The tangent of f(x)=e^{4x}cos(pix),\at x=0 is y=4x+1

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tangent of f(x)=e^{4x}cos(pix),\at x=0

tangent of

f (x) = e^{4 x} cos (π x), at x = 0

y = 4 x + 1

Solution steps

Find the tangent point:

(0, 1)

Find the slope of

f (x) = e^{4 x} cos (π x) : \frac{df ( x )}{d x} = 4 e^{4 x} cos (π x) - π e^{4 x} sin (π x)

Compute the slope of

f (x) = e^{4 x} cos (π x)

x = 0 : m = 4

Find the line with slope m=

4

and passing through

(0, 1) : y = 4 x + 1

y = 4 x + 1

cos (3 x)

\int x^{9} + 8 d x

x y^{^{'}} = 7

\frac{\partial}{\partial y} (3 x^{2} e^{x^{2} y})

f (x) = cos (x), 0, \frac{π}{2}

What is the tangent of f(x)=e^{4x}cos(pix),\at x=0 ?
The tangent of f(x)=e^{4x}cos(pix),\at x=0 is y=4x+1