What is the tangent of f(x) 7/x ,\at a=3 ?

The tangent of f(x) 7/x ,\at a=3 is y=7(((df)/(da))/a-(f(a)}{a^2})x+(14f(a))/a-7\frac{df)/(da)

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tangent of f(x) 7/x ,\at a=3

tangent of

f (x) \frac{7}{x}, at a = 3

y = 7 (\frac{\frac{df}{d a}}{a} - \frac{f ( a )}{a ^{2}}) x + \frac{14 f ( a )}{a} - 7 \frac{df}{d a}

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, \frac{7 f ( a )}{a})

Find the slope of

y = f (x) \frac{7}{x} : \frac{d y}{d x} = 7 (\frac{\frac{df}{d x}}{x} - \frac{f ( x )}{x ^{2}})

Compute the slope of

y = f (x) \frac{7}{x}

x = a : m = 7 (\frac{\frac{df}{d a}}{a} - \frac{f ( a )}{a ^{2}})

Find the line with slope m=

7 (\frac{\frac{df}{d a}}{a} - \frac{f ( a )}{a ^{2}})

and passing through

(a, \frac{7 f ( a )}{a}) : y = 7 (\frac{\frac{df}{d a}}{a} - \frac{f ( a )}{a ^{2}}) x + \frac{14 f ( a )}{a} - 7 \frac{df}{d a}

y = 7 (\frac{\frac{df}{d a}}{a} - \frac{f ( a )}{a ^{2}}) x + \frac{14 f ( a )}{a} - 7 \frac{df}{d a}

\int \frac{e ^{9 x}}{e ^{9 x} + 8} d x

y = e^{x}, y = x e^{x}, x = 0

(\frac{- ln ( 1 + 6 x )}{x})^{^{'}}

\int (2 x - 1) e^{x} d x

f (x) = x^{2} - 2 x + 3

What is the tangent of f(x) 7/x ,\at a=3 ?
The tangent of f(x) 7/x ,\at a=3 is y=7(((df)/(da))/a-(f(a)}{a^2})x+(14f(a))/a-7\frac{df)/(da)