What is the tangent of f(x)=e^{5x}cos(pix),\at x=0 ?

The tangent of f(x)=e^{5x}cos(pix),\at x=0 is y=5x+1

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tangent of f(x)=e^{5x}cos(pix),\at x=0

tangent of

f (x) = e^{5 x} cos (π x), at x = 0

y = 5 x + 1

Solution steps

Find the tangent point:

(0, 1)

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 = 0 : m = 5

Find the line with slope m=

5

and passing through

(0, 1) : y = 5 x + 1

y = 5 x + 1

f (x) = x^{\frac{3}{2}}

\frac{x ^{3}}{x ^{2} + 12}

y y^{^{'}} = 8 sin (x)

\frac{d}{d x} (\frac{x}{( x - 8 ) ^{2}})

f (x) = e^{x}, at x = ln (12)

What is the tangent of f(x)=e^{5x}cos(pix),\at x=0 ?
The tangent of f(x)=e^{5x}cos(pix),\at x=0 is y=5x+1