What is the tangent of y=x^4+4e^x ?

The tangent of y=x^4+4e^x is y=(4a_{0}^3+4e^{a_{0}})x-3a_{0}^4-4a_{0}e^{a_{0}}+4e^{a_{0}}

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tangent of y=x^4+4e^x

tangent of

y = x^{4} + 4 e^{x}

y = (4 a_{0}^{3} + 4 e^{a_{0}}) x - 3 a_{0}^{4} - 4 a_{0} e^{a_{0}} + 4 e^{a_{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{4} + 4 e^{a_{0}})

Find the slope of

y = x^{4} + 4 e^{x} : \frac{d y}{d x} = 4 x^{3} + 4 e^{x}

Compute the slope of

y = x^{4} + 4 e^{x}

x = a_{0} : m = 4 a_{0}^{3} + 4 e^{a_{0}}

Find the line with slope m=

4 a_{0}^{3} + 4 e^{a_{0}}

and passing through

(a_{0}, a_{0}^{4} + 4 e^{a_{0}}) : y = (4 a_{0}^{3} + 4 e^{a_{0}}) x - 3 a_{0}^{4} - 4 a_{0} e^{a_{0}} + 4 e^{a_{0}}

y = (4 a_{0}^{3} + 4 e^{a_{0}}) x - 3 a_{0}^{4} - 4 a_{0} e^{a_{0}} + 4 e^{a_{0}}

\int (2 x sin (y) - y sin (x)) d x

\frac{d}{d x} ((8 x^{2} - 14 x) e^{x})

\int_{1}^{25} e^{x} d x

\frac{d}{d x} (ln ((x + 3)^{4}))

x \to \frac{1}{2} lim (\frac{1}{( 2 x - 1 )})

What is the tangent of y=x^4+4e^x ?
The tangent of y=x^4+4e^x is y=(4a_{0}^3+4e^{a_{0}})x-3a_{0}^4-4a_{0}e^{a_{0}}+4e^{a_{0}}