What is the tangent of y=(3x)/(2^x),\at x=2 ?

The tangent of y=(3x)/(2^x),\at x=2 is y=(3(1-2ln(2)))/4 x+3ln(2)

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tangent of y=(3x)/(2^x),\at x=2

tangent of

y = \frac{3 x}{2 ^{x}}, at x = 2

y = \frac{3 ( 1 - 2 ln ( 2 ) )}{4} x + 3 ln (2)

Solution steps

Find the tangent point:

(2, \frac{3}{2})

Find the slope of

y = \frac{3 x}{2 ^{x}} : \frac{d y}{d x} = \frac{3 ( 1 - ln ( 2 ) x )}{2 ^{x}}

Compute the slope of

y = \frac{3 x}{2 ^{x}}

x = 2 : m = \frac{3 ( 1 - 2 ln ( 2 ) )}{4}

Find the line with slope m=

\frac{3 ( 1 - 2 ln ( 2 ) )}{4}

and passing through

(2, \frac{3}{2}) : y = \frac{3 ( 1 - 2 ln ( 2 ) )}{4} x + 3 ln (2)

y = \frac{3 ( 1 - 2 ln ( 2 ) )}{4} x + 3 ln (2)

\int \frac{e ^{x} + 1}{e ^{2 x} - 1} d x

(\frac{x ^{2} - 2}{5 x ^{3} + 6})^{^{'}}

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 5, y^{^{'}} (0) = 10

\frac{\partial}{\partial x} (tanh (x))

x \to 0 lim (\frac{tan ( 5 x )}{x})

What is the tangent of y=(3x)/(2^x),\at x=2 ?
The tangent of y=(3x)/(2^x),\at x=2 is y=(3(1-2ln(2)))/4 x+3ln(2)