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

,
Find and evaluate at and to find the slope of the tangent line at and .
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.
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 .
Simplify the expression.
Multiply by .
Divide by .
Plug in the slope of the tangent line and the and values of the point into the pointslope formula .
Simplify.
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)

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