Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions

Question 1

Chain Rule

Answer 1

f’(y) = f’(y) / dy * dy / dx

Question 2

Derivative of lny / dx

Answer 2

1/y * dy/dx

Question 3

Find derivatives of:
1. arcsin(x)
2. arccos(x)
3. arctan(x)
4. arccot(x)
5. arcsec(x)
6. arccosec(x)

Answer 3

1. 1 / root (1-x^2)
2. -1 / root (1-x^2)
3. 1 / (1+x^2)
4. -1 / (1+x^2)
5. 1 / (x)(root (x^2-1))
6. -1 / (x)(root (x^2-1))

Question 4

Derivative of inverse of a function

Answer 4

1. Replace y = f(x) {Replace to find in terms of y}
2. Now replace it as f-1 (x)
3. Derivative is: 1 / f ‘ (f-1 (a)) at point a