What is the tangent of e^{x^5} ?

The tangent of e^{x^5} is y=e^{a_{0}^5}*5a_{0}^4x+e^{a_{0}^5}-5a_{0}^5e^{a_{0}^5}

tangent of e^{x^5}

tangent of

e^{x^{5}}

y = e^{a_{0}^{5}} \cdot 5 a_{0}^{4} x + e^{a_{0}^{5}} - 5 a_{0}^{5} e^{a_{0}^{5}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, e^{a_{0}^{5}})

Find the slope of

y = e^{x^{5}} : \frac{d y}{d x} = e^{x^{5}} \cdot 5 x^{4}

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}^{5}} \cdot 5 a_{0}^{4}

Find the line with slope m=

e^{a_{0}^{5}} 5 a_{0}^{4}

and passing through

(a_{0}, e^{a_{0}^{5}}) : y = e^{a_{0}^{5}} \cdot 5 a_{0}^{4} x + e^{a_{0}^{5}} - 5 a_{0}^{5} e^{a_{0}^{5}}

y = e^{a_{0}^{5}} \cdot 5 a_{0}^{4} x + e^{a_{0}^{5}} - 5 a_{0}^{5} e^{a_{0}^{5}}

\frac{d}{d x} (8 x^{2} + 7)

\int_{0}^{2} 3^{- x} d x

y^{^{''}} - 2 y^{^{'}} + 10 y = e^{x} cos (3 x)

\int sin (u^{2}) d u

\frac{\partial}{\partial y} (\frac{2 y}{x ^{2} + y ^{2}})

What is the tangent of e^{x^5} ?
The tangent of e^{x^5} is y=e^{a_{0}^5}*5a_{0}^4x+e^{a_{0}^5}-5a_{0}^5e^{a_{0}^5}