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n^th Derivative
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The nth derivative of a function, written \(f^{\left(n\right)}\left(x\right)\) or \(\frac{d^{n}y}{dx^{n}}\), found by differentiating \(n\) times.
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n^th Derivative
AHL 5.12
The nth derivative of f is
f(n)(x)=f′′′′…′′n times(x)🚫
dxndny=dxd(dxd(…dxd(y)))n times🚫
For example, look at the notation in use below:
f(x)=x5 dxdf′(x)=5x4dxdf(2)(x)=20x3dxdf(3)(x)=60x2dxdf(4)(x)=120xdxdf(5)(x)=120.
The IB often tests higher order derivatives by giving nth power proofs, which involve induction.
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