What is the tangent of (3x-1)/(e^x) ?

The tangent of (3x-1)/(e^x) is y=(-3a_{0}+4)/(e^{a_{0)}}x+(3a_{0}^2-a_{0}-1)/(e^{a_{0)}}

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tangent of (3x-1)/(e^x)

tangent of

\frac{3 x - 1}{e ^{x}}

y = \frac{- 3 a _{0} + 4}{e ^{a_{0}}} x + \frac{3 a _{0}^{2} - a _{0} - 1}{e ^{a_{0}}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{3 a _{0} - 1}{e ^{a_{0}}})

Find the slope of

y = \frac{3 x - 1}{e ^{x}} : \frac{d y}{d x} = \frac{- 3 x + 4}{e ^{x}}

Compute the slope of

y = \frac{3 x - 1}{e ^{x}}

x = a_{0} : m = \frac{- 3 a _{0} + 4}{e ^{a_{0}}}

Find the line with slope m=

\frac{- 3 a _{0} + 4}{e ^{a_{0}}}

and passing through

(a_{0}, \frac{3 a _{0} - 1}{e ^{a_{0}}}) : y = \frac{- 3 a _{0} + 4}{e ^{a_{0}}} x + \frac{3 a _{0}^{2} - a _{0} - 1}{e ^{a_{0}}}

y = \frac{- 3 a _{0} + 4}{e ^{a_{0}}} x + \frac{3 a _{0}^{2} - a _{0} - 1}{e ^{a_{0}}}

\frac{\partial}{\partial x} (1 - \frac{y}{x})

x (cos (x^{2}))

\frac{( x ^{2} - 4 )}{( x ^{2} - 1 )}

\int \frac{9 x ^{2} - 8 x + 8}{x ( x ^{2} + 4 )} d x

n = 0 \sum \infty \frac{n}{n + 2}

What is the tangent of (3x-1)/(e^x) ?
The tangent of (3x-1)/(e^x) is y=(-3a_{0}+4)/(e^{a_{0)}}x+(3a_{0}^2-a_{0}-1)/(e^{a_{0)}}