Final answer to the problem
$y=\sqrt{25-x^2},\:y=-\sqrt{25-x^2}$
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Step-by-step Solution
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- Solve for x
- Solve for y
- Find the derivative
- Solve by implicit differentiation
- Solve for y'
- Find dy/dx
- Derivative
- Find the derivative using the definition
- Solve by quadratic formula (general formula)
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1
We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $x^2$ from both sides of the equation
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$y^2=25-x^2$
Learn how to solve equations problems step by step online. Solve the equation x^2+y^2=25. We need to isolate the dependent variable y, we can do that by simultaneously subtracting x^2 from both sides of the equation. Removing the variable's exponent. Cancel exponents 2 and 1. As in the equation we have the sign \pm, this produces two identical equations that differ in the sign of the term \sqrt{25-x^2}. We write and solve both equations, one taking the positive sign, and the other taking the negative sign.
Final answer to the problem
$y=\sqrt{25-x^2},\:y=-\sqrt{25-x^2}$
