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

Math
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Find and evaluate at and to find the slope of the tangent line at and .
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Use to rewrite as .
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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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 .
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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.
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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.
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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 .
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Replace the variable with in the expression.
Simplify each term.
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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 pointslope formula .
Simplify.
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The slope-intercept form is , where is the slope and is the y-intercept.
Rewrite in slope-intercept form.
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Multiply by .
Simplify .
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Multiply by .
Apply the distributive property.
Multiply by .
Move all terms not containing to the right side of the equation.
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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)

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