,

Use to rewrite as .

Differentiate both sides of the equation.

The derivative of with respect to is .

Differentiate the right side of the equation.

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

Evaluate .

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 .

Evaluate .

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

Differentiate using the Power Rule which states that is where .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Combine and .

Combine and .

Move to the denominator using the negative exponent rule .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

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

Replace with .

Evaluate at and .

Replace the variable with in the expression.

Simplify each term.

One to any power is one.

Divide by .

Multiply by .

Subtract from .

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.

Multiply by .

Simplify .

Multiply by .

Apply the distributive property.

Multiply by .

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Add and .

Find the Tangent Line at the Point y=9x-8 square root of x , (1,1)