# Calculus Examples

Find the Tangent Line at the Point y=(7x)/(x-1) , (2,14)
,
Step 1
Find the first derivative and evaluate at and to find the slope of the tangent line.
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Quotient Rule which states that is where and .
Differentiate.
Differentiate using the Power Rule which states that is where .
Multiply by .
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 .
Simplify terms.
Multiply by .
Subtract from .
Simplify the expression.
Subtract from .
Move the negative in front of the fraction.
Multiply by .
Combine and .
Move the negative in front of the fraction.
Evaluate the derivative at .
Simplify.
Simplify the denominator.
Subtract from .
One to any power is one.
Simplify the expression.
Divide by .
Multiply by .
Step 2
Plug the slope and point values into the point-slope formula and solve for .
Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Simplify the equation and keep it in point-slope form.
Solve for .
Simplify .
Rewrite.