Final answer to the problem
$y=-4+\sqrt{\frac{-64x^2+640x-16z^2-128z-2624}{64}+16},\:y=-4-\sqrt{\frac{-64x^2+640x-16z^2-128z-2624}{64}+16}$
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Step-by-step Solution
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- Solve for x
- Solve for y
- Solve for z
- Find the derivative
- Solve by implicit differentiation
- Solve for y'
- Find dy/dx
- Derivative
- Find the derivative using the definition
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1
Group the terms of the equation
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$64y^2+512y=-64x^2+640x-16z^2-128z-2624$
Learn how to solve problems step by step online. Solve the quadratic equation 64x^2-640x64y^2512y16z^2128z+2624=0. Group the terms of the equation. Factor the polynomial 64y^2+512y by it's greatest common factor (GCF): 64y. Divide both sides of the equation by 64. Multiplying polynomials y and y+8.
Final answer to the problem
$y=-4+\sqrt{\frac{-64x^2+640x-16z^2-128z-2624}{64}+16},\:y=-4-\sqrt{\frac{-64x^2+640x-16z^2-128z-2624}{64}+16}$
