# Differentiation – Further Pure Maths 2

Candidates should be able to:

• differentiate hyperbolic functions and differentiate sin–1x, cos–1x, sinh–1x, cosh–1x and tanh–1x
• obtain an expression for $$\frac{d^2y}{dx^2}$$ in cases where the relation between x and y is defined implicitly or parametrically
• derive and use the first few terms of a Maclaurin’s series for a function. (Derivation of a general term is not included, but successive ‘implicit’ differentiation steps may be required, e.g. for y = tan x following an initial differentiation rearranged as y′= 1 + y2.)

Differentiation – Further Pure Maths 2 Video (2 Parts)