Differentiation

Question 1

d/dx sec(x)

Answer 1

sec(x)tan(x)

Question 2

d/dx cosec(x)

Answer 2

-cosec(x)cot(x)

Question 3

d/dx cot(x)

Answer 3

-cosec²(x)

Question 4

d/dx a^ux

Answer 4

lna × a^ux × d/dx ux

(ln number × original expression × differentiate power)

Question 5

d/dx y²

Answer 5

d/dy y² × dy/dx
= 2y dy/dx

Question 6

d/dx y³

Answer 6

3y² dy/dx

Question 7

d/dx xy

Answer 7

x dy/dx + y

(chain rule)

Question 8

d/dx sin-1[f(x)]

Answer 8

[f’(x)]/√{1-[f(x)]²}

Question 9

d/dx cos^-1 f(x)

Answer 9

• f’(x)/root 1-[f(x)]²]

Question 10

d/dx tan^-1 f(x)

Answer 10

f’(x)/1+[f(x)]²