What is the tangent of f(x)=e^{1+2tan(x)},\at x= pi/4 ?

The tangent of f(x)=e^{1+2tan(x)},\at x= pi/4 is y=4e^3x+e^3-e^3pi

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tangent of f(x)=e^{1+2tan(x)},\at x= pi/4

tangent of

f (x) = e^{1 + 2 t a n (x)}, at x = \frac{π}{4}

y = 4 e^{3} x + e^{3} - e^{3} π

Solution steps

Find the tangent point:

(\frac{π}{4}, e^{3})

Find the slope of

f (x) = e^{1 + 2 t a n (x)} : \frac{df ( x )}{d x} = e^{1 + 2 t a n (x)} \cdot 2 sec^{2} (x)

Compute the slope of

f (x) = e^{1 + 2 t a n (x)}

x = \frac{π}{4} : m = 4 e^{3}

Find the line with slope m=

4 e^{3}

and passing through

(\frac{π}{4}, e^{3}) : y = 4 e^{3} x + e^{3} - e^{3} π

y = 4 e^{3} x + e^{3} - e^{3} π

t \cdot sin (k \cdot t)

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

x \to - 4 lim (- 5 x - 8)

\frac{d}{d x} (x^{2} (6 - x))

x y^{^{'}} - 2 y = x^{2} - x - 2

What is the tangent of f(x)=e^{1+2tan(x)},\at x= pi/4 ?
The tangent of f(x)=e^{1+2tan(x)},\at x= pi/4 is y=4e^3x+e^3-e^3pi