What is the tangent of f(x)=e^{5x}cos(pix),\at x=1 ?

The tangent of f(x)=e^{5x}cos(pix),\at x=1 is y=-5e^5x+4e^5

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tangent of f(x)=e^{5x}cos(pix),\at x=1

tangent of

f (x) = e^{5 x} cos (π x), at x = 1

y = - 5 e^{5} x + 4 e^{5}

Solution steps

Find the tangent point:

(1, - e^{5})

Find the slope of

f (x) = e^{5 x} cos (π x) : \frac{df ( x )}{d x} = 5 e^{5 x} cos (π x) - π e^{5 x} sin (π x)

Compute the slope of

f (x) = e^{5 x} cos (π x)

x = 1 : m = - 5 e^{5}

Find the line with slope m=

- 5 e^{5}

and passing through

(1, - e^{5}) : y = - 5 e^{5} x + 4 e^{5}

y = - 5 e^{5} x + 4 e^{5}

\int - 2 e^{x} d x

\frac{d}{d x} (- 6 sin (2 x) + 3 cos (3 x))

\frac{d}{d x} (x (55 - 0.5 x) - 110)

\frac{d}{d t} (e^{3 i t})

\int \frac{x ^{3}}{x ^{2} - 100} d x

What is the tangent of f(x)=e^{5x}cos(pix),\at x=1 ?
The tangent of f(x)=e^{5x}cos(pix),\at x=1 is y=-5e^5x+4e^5