Question

Finding an Equation of a Tangent Line In Exercise, find an equation of the tangent line to the graph of the function at the given point. See Example 5.
y = ln x3; (1, 0)

Answer 1

Answer:

$y=3x-3$

Step-by-step explanation:

We are given that

$y=ln x^3$

Point (1,0)

We have to find the equation of tangent line to the given graph.

Differentiate w.r.t x

$\frac{dy}{dx}=\frac{1}{x^3}\times 3x^2}=\frac{3}{x}$

$\frac{d(lnx)}{dx}=\frac{1}{x}$

Substitute x=1

$m=\frac{dy}{dx}=3$

Slope-point form:

$y-y_1=m(x-x_1)$

$x_1=1,y_1=0$

By using this formula

The equation of tangent to the given graph

$y-0=3(x-1)=3x-3$

$y=3x-3$