1. Find an equation of the tangent line to the graph of the logarithmic function

Question

1. Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y = ln x3

2. Find the derivative of the function. f(x) = 6x2 ln 6x. f '(x)=?

3. Find the derivative of the function. y = ln(x?x2 – 4). y' =?

4. Find the derivative of the function. f(x) = ln(6x / (x+1)). f '(x) =?

6. Use implicit differentiation to find dy/dx. ln xy + 2x = 25. dy/dx=?

7. Use implicit differentiation to find an equation of the tangent line to the graph at the given point. x + y ? 1 = ln(x11 + y18),    (1, 0). y=?

10. Use logarithmic differentiation to find dy/dx. y = ((x + 1)(x ? 10))/((x ? 1)(x + 10)) , x > 10. dy/dx=?

11. Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) .

12. Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) .

13. Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

14. Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

15. Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

16. Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

Explanation / Answer

1) y =ln x^3 = 3ln x

Slope of the tangent = dy/dx = d/dx( 3ln x) = 3 /x

Slope of the tangent at the point (1,0) = 3/1 =3

Equation of a line in point -slope form is y -y1 = m(x-x1)

Equation of the tangent line with slope =3 and passing through the point (1,0) is

y -0 = 3(x -1)

y = 3x -3

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