Implicit Differentiation - Worksheet 4 | MATH 165, Assignments of Calculus

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Math 165: Worksheet #4 – Implicit Differentiation

Find the dy dx of the following functions:

1.) y^2 = x

2.) 3x^2 + y^2 = 14

3.) 6x^2 − 4 x + 5y^2 + 4y = 9

4.) (2x − 3)^2 + (4y − 5)^2 = 10

5.) x^2 sin (x) + y^2 cos (y) = 1

6.) x^2 y^2 = 1

7.) y^2 tan (x) = x

8.) x^2 csc (y) = y

9.) 4x^2 + 3xy^2 − 6 x^2 y = y^3

10.) 5xy^3 + 5x^3 y + 3x^5 y + 3xy^5 = 15xy

Solutions:

2 y

2. − 3 x y

2 − 6 x 2 + 5y

3 − 2 x 8 y − 10

5. − 2 x sin (x) + x^2 cos (x) 2 y cos (y) − y^2 sin (y)

6. − y x

1 − y^2 sec^2 (x) 2 y tan (x)

2 x csc (y) 1 + x^2 csc (y) cot (y)

8 x + 3y^2 − 12 xy 3 y^2 + 6x^2 − 6 xy

15 y − 5 y^3 − 15 x^2 y − 15 x^4 y − 3 y^5 15 xy^2 + 5x^3 + 3x^5 + 15xy^4 − 15 x

− 2 y^5 /^2 1 + 4xy^3 /^2

−2(y + 2) x

tan (y) sec^2 (y)

tan (y) y sec^2 (y)