What is the tangent of 18e^x+15x ?

The tangent of 18e^x+15x is y=(18e^{a_{0}}+15)x-18a_{0}e^{a_{0}}+18e^{a_{0}}

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tangent of 18e^x+15x

tangent of

18 e^{x} + 15 x

y = (18 e^{a_{0}} + 15) x - 18 a_{0} e^{a_{0}} + 18 e^{a_{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 18 e^{a_{0}} + 15 a_{0})

Find the slope of

y = 18 e^{x} + 15 x : \frac{d y}{d x} = 18 e^{x} + 15

Compute the slope of

y = 18 e^{x} + 15 x

x = a_{0} : m = 18 e^{a_{0}} + 15

Find the line with slope m=

18 e^{a_{0}} + 15

and passing through

(a_{0}, 18 e^{a_{0}} + 15 a_{0}) : y = (18 e^{a_{0}} + 15) x - 18 a_{0} e^{a_{0}} + 18 e^{a_{0}}

y = (18 e^{a_{0}} + 15) x - 18 a_{0} e^{a_{0}} + 18 e^{a_{0}}

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

(ln (x^{2}))^{^{'}}

\frac{d}{d x} (\frac{( 2 )}{( 6 - 12 x )})

5 cos (π x), 12 x^{2} - 3, - 0.5, 0.5

\frac{d}{d x} (2 y x)

What is the tangent of 18e^x+15x ?
The tangent of 18e^x+15x is y=(18e^{a_{0}}+15)x-18a_{0}e^{a_{0}}+18e^{a_{0}}