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

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

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tangent of e^{x^2}

tangent of

e^{x^{2}}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = e^{x^{2}}

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

Find the line with slope m=

e^{a_{0}^{2}} 2 a_{0}

and passing through

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

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

\int 2 sin (5 x) d x

e^{t} cos (5 t)

2 x (x + 1)^{3} (x^{2} + 2 x + 1)^{2}

(1 + x^{2})^{\frac{3}{2}} x

\int \frac{3}{5 - 2 x} d x

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