Implicit Differentiation - [Pure 4].

Question 1

What order do you do things to solve using Implicit Differentiation?

Answer 1

1. Differentiate with respect to x.
2. Collect the dy/dx terms on one side.
3. Solve for dy/dx.

Question 2

What is y² differentiated with respect to x?

Answer 2

• u = y².
• du/dy = 2y.
• d(y²)/dx = 2y(dy/dx).

Question 3

When y = a^x, what does dy/dx equal?

Answer 3

dy/dx = a^xln(a).

Question 4

What rule may you need to use if you have terms with y and x?

Answer 4

Product Rule.

Question 5

What does ‘y’ implicitly differentiate to?

Answer 5

dy/dx.

Question 6

What does ‘y³’ implicitly differentiate to?

Answer 6

3y(dy/dx).

Question 7

What does 8y² implicitly differentiate to?

Answer 7

16y(dy/dx).

Question 8

If a tangent is parallel to the x-axis what does dy/dx equal?

Answer 8

Zero (0).

Question 9

If a tangent is parallel to the y-axis what does dy/dx equal?

Answer 9

Zero (0).

Question 10

For a stationary point, dy/dx = ___?

Answer 10

Zero (0).

Question 11

What equals Zero (0) for a Point of Inflection?

Answer 11

Second Derivative: d²y/dx².

Question 12

What happens when you implicitly differentiate tan(y)?

Answer 12

tan(y) = (sec²(y)) (dy/dx).

Question 13

What happens when you implicitly differentiate sin(y²)?

Answer 13

sin(y²) = (-2cos(y)) (dy/dx).

Question 14

What happens when you implicitly differentiate cos(3y)?

Answer 14

cos(3y) = (-3sin(3y)) (dy/dx).

Question 15

What happens when you implicitly differentiate e^2x?

Answer 15

e^2x = 2e^2x.

Only has x terms, no y terms.