What is the tangent of x+e^{2x} ?

The tangent of x+e^{2x} is y=(1+e^{2a_{0}}*2)x-2a_{0}e^{2a_{0}}+e^{2a_{0}}

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tangent of x+e^{2x}

tangent of

x + e^{2 x}

y = (1 + e^{2 a_{0}} \cdot 2) x - 2 a_{0} e^{2 a_{0}} + e^{2 a_{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} + e^{2 a_{0}})

Find the slope of

y = x + e^{2 x} : \frac{d y}{d x} = 1 + e^{2 x} \cdot 2

Compute the slope of

y = x + e^{2 x}

x = a_{0} : m = 1 + e^{2 a_{0}} \cdot 2

Find the line with slope m=

1 + e^{2 a_{0}} 2

and passing through

(a_{0}, a_{0} + e^{2 a_{0}}) : y = (1 + e^{2 a_{0}} \cdot 2) x - 2 a_{0} e^{2 a_{0}} + e^{2 a_{0}}

y = (1 + e^{2 a_{0}} \cdot 2) x - 2 a_{0} e^{2 a_{0}} + e^{2 a_{0}}

(0, 0), (5, 1)

(2 x - 5)^{4} (x^{2} + x + 1)^{5}

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

\frac{d}{d x} (ln (2 x))

y^{^{''}} - 5 y^{^{'}} + 4 y = 8 e^{x}

What is the tangent of x+e^{2x} ?
The tangent of x+e^{2x} is y=(1+e^{2a_{0}}*2)x-2a_{0}e^{2a_{0}}+e^{2a_{0}}