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August 31st, 2015, 06:03 AM   #1
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Angry Implicit Function

I tried to solve these ones, but ended up with some weird results ... so any help?

1st one: x^(2)*(y^2 + 1) = 5

Prove that: x^3 y dy/dx + 5 = 0 !!

2nd : y = sqrt(1 + sqrt(x + sqrt(x)))

Prove that: dy/dx = (2 sqrt(x) + 1)/(8y (y^2 - 1) sqrt(x))

and last one ...

Find the angle between the target of the curve

x^2 + 3xy + y^2 = 5 at point (1,1)

Last edited by skipjack; August 31st, 2015 at 08:25 AM.
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August 31st, 2015, 08:22 AM   #2
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1st one: differentiating gives x²(2y dy/dx) + 2x(y² + 1) = 0.
Multiplying that by x/2 gives x³y dy/dx + x²(y² + 1) = 0, and the desired result follows.

Hint for 2nd one: show that (y² - 1)² = x + √x, then differentiate.

What does "the angle between the target of the curve" mean?
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