What is the tangent of f(x)=1+ln(2x-1),\at x=1 ?

The tangent of f(x)=1+ln(2x-1),\at x=1 is y=2x-1

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tangent of f(x)=1+ln(2x-1),\at x=1

tangent of

f (x) = 1 + ln (2 x - 1), at x = 1

y = 2 x - 1

Solution steps

Find the tangent point:

(1, 1)

Find the slope of

f (x) = 1 + ln (2 x - 1) : \frac{df ( x )}{d x} = \frac{2}{2 x - 1}

Compute the slope of

f (x) = 1 + ln (2 x - 1)

x = 1 : m = 2

Find the line with slope m=

2

and passing through

(1, 1) : y = 2 x - 1

y = 2 x - 1

x^{2} + y^{2} = 25

(23, 2)

y = x^{2} - x^{3} + x, (- 2, 10)

(- 2.4) (7.3)

e^{2 x}

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