Section 2.6 Homework

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Section 2.6 Homework

1. Consider the following equation.

5 x^{2} - y^{2} = 3

(a) Find y’ by implicit differentiation.

(b) Solve the equation explicitly for y and differentiate to get y’ in terms of x.

2. Find dy/dx by implicit differentiation.

$x^{2} - 4 x y + y^{2} = 4$

3. Find dy/dx by implicit differentiation.

$\frac{x^{2}}{x + y} = y^{2} + 5$

4. Find dy/dx by implicit differentiation.

$y \cos (x) = 2 x^{2} + 5 y^{2}$

5. Find dy/dx by implicit differentiation.

$\cos (x y) = 1 + \sin (y)$

6. Find dy/dx by implicit differentiation.

$\sqrt{7 x y} = 6 + x^{2} y$

7 Find dy/dx by implicit differentiation.

$x \sin (y) + y \sin (x) = 4$

8 Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy.

$x^{5} y^{2} - x^{5} y + 5 x y^{3} = 0$

9. Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy.

y sec(x) = 6x tan(y)

10. Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

11. Find y” by implicit differentiation.

$x^{2} + 2 y^{2} = 2$

12. If

x^{2} + x y + y^{3} = 1

find the value of y”’ at the point where x = 1.

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This question is taken from Math 261 – Calculus I » Spring 2022 » Homeworks

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