What is the tangent of 6-2e^x ?

The tangent of 6-2e^x is y=-2e^{a_{0}}x+6-2e^{a_{0}}+2a_{0}e^{a_{0}}

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tangent of 6-2e^x

tangent of

6 - 2 e^{x}

y = - 2 e^{a_{0}} x + 6 - 2 e^{a_{0}} + 2 a_{0} e^{a_{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 6 - 2 e^{a_{0}})

Find the slope of

y = 6 - 2 e^{x} : \frac{d y}{d x} = - 2 e^{x}

Compute the slope of

y = 6 - 2 e^{x}

x = a_{0} : m = - 2 e^{a_{0}}

Find the line with slope m=

- 2 e^{a_{0}}

and passing through

(a_{0}, 6 - 2 e^{a_{0}}) : y = - 2 e^{a_{0}} x + 6 - 2 e^{a_{0}} + 2 a_{0} e^{a_{0}}

y = - 2 e^{a_{0}} x + 6 - 2 e^{a_{0}} + 2 a_{0} e^{a_{0}}

x \to 0 lim (2 cos (\frac{π}{x}))

\int_{1}^{\infty} \frac{1}{x ^{5}} d x

\int \frac{ln ( 8 x )}{x} d x

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

\frac{d}{d x} (sin (x) + \frac{4}{9} cot (x))

What is the tangent of 6-2e^x ?
The tangent of 6-2e^x is y=-2e^{a_{0}}x+6-2e^{a_{0}}+2a_{0}e^{a_{0}}