,

Differentiate both sides of the equation.

The derivative of with respect to is .

Differentiate the right side of the equation.

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

Differentiate.

By the Sum Rule, the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Since is constant with respect to , the derivative of with respect to is .

Simplify the expression.

Add and .

Reorder the factors of .

Reform the equation by setting the left side equal to the right side.

Simplify.

Multiply and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Replace with .

Evaluate at and .

Replace the variable with in the expression.

Subtract from .

Simplify the denominator.

Raise to the power of .

Multiply by .

Subtract from .

Add and .

Simplify the expression.

Multiply by .

Divide by .

Plug in the slope of the tangent line and the and values of the point into the point–slope formula .

The slope-intercept form is , where is the slope and is the y-intercept.

Rewrite in slope-intercept form.

Subtract from .

Simplify .

Multiply by .

Apply the distributive property.

Multiply by .

Find the Tangent Line at (8,0) y = natural log of x^2-8x+1 , (8,0)