What is the tangent of e^{x^3} ?

The tangent of e^{x^3} is y=e^{a_{0}^3}*3a_{0}^2x+e^{a_{0}^3}-3a_{0}^3e^{a_{0}^3}

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tangent of e^{x^3}

tangent of

e^{x^{3}}

y = e^{a_{0}^{3}} \cdot 3 a_{0}^{2} x + e^{a_{0}^{3}} - 3 a_{0}^{3} e^{a_{0}^{3}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, e^{a_{0}^{3}})

Find the slope of

y = e^{x^{3}} : \frac{d y}{d x} = e^{x^{3}} \cdot 3 x^{2}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = e^{a_{0}^{3}} \cdot 3 a_{0}^{2}

Find the line with slope m=

e^{a_{0}^{3}} 3 a_{0}^{2}

and passing through

(a_{0}, e^{a_{0}^{3}}) : y = e^{a_{0}^{3}} \cdot 3 a_{0}^{2} x + e^{a_{0}^{3}} - 3 a_{0}^{3} e^{a_{0}^{3}}

y = e^{a_{0}^{3}} \cdot 3 a_{0}^{2} x + e^{a_{0}^{3}} - 3 a_{0}^{3} e^{a_{0}^{3}}

\frac{\partial}{\partial x} (e^{x y z^{3}})

\int t ln (t + 5) d t

\int \frac{x}{1 + 2 x ^{2}} d x

\frac{d}{d x} (x^{5} + 3 x^{2} + 1)

10 x, x^{2} - 11

What is the tangent of e^{x^3} ?
The tangent of e^{x^3} is y=e^{a_{0}^3}*3a_{0}^2x+e^{a_{0}^3}-3a_{0}^3e^{a_{0}^3}