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How do you find the derivitive of a funtion that has more than one unknown variable?
Find dy/dx using implicit differentiation.
Start by using the Product Rule on the two terms on the left.
We take the derivative of both sides to obtain
(x2) ′y + x2y′ + x′y2 + x(y2) ′ = (3x) ′ .
Then, we simplify to
2xy + x2y′ + y2 + x2yy′ = 3
2xy + x2y′ + y2 + 2xyy′ = 3.
Solve for y′ by placing all y′ terms on one side.
Rearranging so that all terms containing y′ are on one side, we have
x2y′ + 2xyy′ = 3 – 2xy – y2
y′ (x2 + 2xy) = 3 – 2xy – y2
Solve for y′ .
You can factor out x from the bottom if you like, but it doesn't really simplify the answer.
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How do you find the derivitive of a funtion that has more than one unknown variable?
Find dy/dx using implicit differentiation.
Start by using the Product Rule on the two terms on the left.
We take the derivative of both sides to obtain
(x2) ′y + x2y′ + x′y2 + x(y2) ′ = (3x) ′ .
Then, we simplify to
2xy + x2y′ + y2 + x2yy′ = 3
2xy + x2y′ + y2 + 2xyy′ = 3.
Solve for y′ by placing all y′ terms on one side.
Rearranging so that all terms containing y′ are on one side, we have
x2y′ + 2xyy′ = 3 – 2xy – y2
y′ (x2 + 2xy) = 3 – 2xy – y2
Solve for y′ .
Solve for y′ .
You can factor out x from the bottom if you like, but it doesn't really simplify the answer.