2 - 7 further calculus

Question 1

differentiateing inverse trig

Answer 1

y = sin^-1 x find dy/dx
siny = x
dx/dy = cosh y
dy/dx = 1/cos y
= 1/root(1-sin^2y)
= 1/root(1-x^2

Question 2

differentiating arccpsh(x/2)

Answer 2

use the definition of d/dx accosh(x)
but replace x with x/2 and times by the derivative of x/2 = 1/2

Question 3

using derivites of inverse trig to get integration results

Answer 3

all in formula booklet except cos^-1 wich is just -sin^-1
and tanh^-1 = ∫1/1-x^2

Question 4

partial fractions with a quadratic denominatpr

Answer 4

• factprise to linear factors
• perfect square also factorises
• doesnt factorise - make numerator Bx + C