,

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 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.

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 .

Add and .

Rewrite in slope-intercept form.

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