# Find the Tangent Line at the Point y = square root of x , (25,5)

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Find and evaluate at and to find the slope of the tangent line at and .
Use to rewrite as .
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
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.
Rewrite the expression using the negative exponent rule .
Multiply and .
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 the denominator.
Rewrite as .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Multiply 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.
Multiply by .
Simplify .
Multiply by .
Apply the distributive property.
Combine and .
Cancel the common factor of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Move the negative in front of the fraction.
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
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 .