What is the tangent of y=x^4+5e^x ?

The tangent of y=x^4+5e^x is y=(4a_{0}^3+5e^{a_{0}})x-3a_{0}^4-5a_{0}e^{a_{0}}+5e^{a_{0}}

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tangent of y=x^4+5e^x

tangent of

y = x^{4} + 5 e^{x}

y = (4 a_{0}^{3} + 5 e^{a_{0}}) x - 3 a_{0}^{4} - 5 a_{0} e^{a_{0}} + 5 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} + 5 e^{a_{0}})

Find the slope of

y = x^{4} + 5 e^{x} : \frac{d y}{d x} = 4 x^{3} + 5 e^{x}

Compute the slope of

y = x^{4} + 5 e^{x}

x = a_{0} : m = 4 a_{0}^{3} + 5 e^{a_{0}}

Find the line with slope m=

4 a_{0}^{3} + 5 e^{a_{0}}

and passing through

(a_{0}, a_{0}^{4} + 5 e^{a_{0}}) : y = (4 a_{0}^{3} + 5 e^{a_{0}}) x - 3 a_{0}^{4} - 5 a_{0} e^{a_{0}} + 5 e^{a_{0}}

y = (4 a_{0}^{3} + 5 e^{a_{0}}) x - 3 a_{0}^{4} - 5 a_{0} e^{a_{0}} + 5 e^{a_{0}}

3 e^{3 e^{x} + x}

\int (e - x - e^{3}) (e x + e - 5) d x

\int_{9}^{x} 1 + 9 t d t

\int sec^{4} (3 x) tan^{2} (3 x) d x

\frac{d}{d x} (lo g_{e} (x^{3}))

What is the tangent of y=x^4+5e^x ?
The tangent of y=x^4+5e^x is y=(4a_{0}^3+5e^{a_{0}})x-3a_{0}^4-5a_{0}e^{a_{0}}+5e^{a_{0}}