1. Gradients of Inverse Trig Functions Use the relationship Ex y = sin –1 x This is the same as siny = x ie sin both sides Sox = siny Differentiate this expression. Remember the letter that comes 1 st goes on top The letter that comes 2 nd goes underneath.

2. x = siny Using sin 2 x + cos 2 x = 1 replace y by x. So sin 2 y + cos 2 y = 1 Make cosy the subject cos 2 y = 1 – sin 2 y But x = sinySo

3. This technique can be used to differentiate y = cos –1 x and y = tan –1 x (use 1 + tan 2 x = sec 2 x) Find the gradient of y = cos –1 x and y = tan –1 x

4. y = sinh x = Differentiating Hyperbolic Functions y = cosh x = y = tanh x = Prove it using the quotient rule

5. Using techniques from C4(DIFIU) y = cosh  x y = sinh 2x y = tanh (3x+2)

6. Differentiating Inverse Hyperbolic Functions y = sinh –1 x sox = sinhy cosh 2 x – sinh 2 x = 1 Using Osbornes Rule

7. Differentiating Inverse Hyperbolic Functions y = cosh –1 x sox = coshy cosh 2 x – sinh 2 x = 1 Using Osbornes Rule

8. Differentiating Inverse Hyperbolic Functions y = tanh –1 x sox = tanhy 1 – tanh 2 x = sech 2 x Using Osbornes Rule See FP2 Notes for further examples