FP3 §2 Differentiation

Question 1

d/dx sinh x

Answer 1

cosh x

Question 2

d/dx(cosh x)

Answer 2

sinh x

Question 3

d/dx (tanh x)

Answer 3

sech²x

Question 4

d/dx( coth x)

Answer 4

- cosech²(x)

Question 5

d/dx sech(x)

Answer 5

• tanh x sech x

Question 6

d/dx arsinh (x)

Answer 6

1/ √(x² + 1)

Question 7

d/dx (arcosh x)

Answer 7

1/ √(x² - 1)

Question 8

d/dx (artanh x)

Answer 8

1/(1 - x²)

Question 9

d/dx (arcsin x)

Answer 9

1/ √(1 - x²)

Question 10

d/dx (arccos x)

Answer 10

(-1) / √(1 - x²)

Question 11

d/dx (arctan x)

Answer 11

1/(1 + x²)

Question 12

d/dx (cosech x)

Answer 12

- (coth x)(cosech x)