Homework

Problem 1 · easy

Find dy/dx for x^2 + y^2 = 1.

Problem 2 · easy

Find dy/dx for x^2 - y^2 = 4.

Problem 3 · easy

Find dy/dx for 2x + 3y = 7.

Problem 4 · easy

Find dy/dx for y^2 = x^3.

Problem 5 · easy

Find dy/dx for x^3 + y^3 = 8.

Problem 6 · easy

Find dy/dx for xy = 5.

Problem 7 · easy

Find dy/dx for x^2 + 4y^2 = 16.

Problem 8 · easy

Find the slope of x^2 + y^2 = 25 at (3, -4).

Problem 9 · easy

Find the slope of x^2 + y^2 = 25 at (0, 5).

Problem 10 · medium

Find dy/dx for x^2*y = 4.

Problem 11 · medium

Find dy/dx for x*y^2 = 3.

Problem 12 · medium

Find dy/dx for x^2 + xy + y^2 = 7.

Problem 13 · medium

Find the tangent line to x^2 + y^2 = 25 at (4, 3). Give the slope.

Problem 14 · challenge

Find dy/dx for y = sin(x + y).

Problem 15 · medium

Find dy/dx for x^2*y^2 = 1.

Problem 16 · challenge

Find dy/dx for x + y = sin(y).

Problem 17 · easy

Find dy/dx for y^3 - x^3 = 9.

Problem 18 · medium

Find dy/dx for x^2 + y = x*y.

Problem 19 · medium

Find dy/dx for sqrt(x) + sqrt(y) = 4.

Problem 20 · challenge

Find dy/dx for sin(x)*cos(y) = 1.

Problem 21 · challenge

For x^2 + y^2 = 25, find d^2y/dx^2.

Problem 22 · challenge

Find dy/dx for e^y = x. (Treat e^y as a chain rule application.)

Problem 23 · medium

Find dy/dx for y^2 + x = 5 at the point (4, 1).

Problem 24 · challenge

Find dy/dx for x*y^3 + x^3*y = 4.

Problem 25 · easy

Find dy/dx for 3x^2 - y^2 = 1.