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Differentiation rules

Differentiation rules - Exercises | IB Math AASL | Perplex

Differentiation rules

Differentiation rules

Power rule, chain rule, product rule, quotient rule, derivatives of ex, ax, loga(x), trigonometric, and inverse trigonometric functions

Want a deeper conceptual understanding? Try our interactive lesson!

Exercises

No exercises available for this concept.

Key Skills

Derivative of xⁿ where n is an integer

SL 5.3

f(x)=xn, n∈Z⇒f′(x)=nxn−1📖

Derivatives of sums and scalar multiples

SL 5.3

dxd(af(x))=af′(x)🚫

dxd(f(x)+g(x))=f′(x)+g′(x)🚫

dxd(af(x)+bg(x))=af′(x)+bg′(x)🚫

Derivative of xⁿ where n is rational

SL 5.6

f(x)=xn, n∈Q⇒f′(x)=nxn−1📖

Chain rule

SL 5.6

(g(f(x)))′=g′(f(x))⋅f′(x)🚫

y=g(u) where u=f(x)

dxdy=dudg⋅dxdu📖

Derivative of e^x

SL 5.6

f(x)=ex⇒f′(x)=ex📖

Derivative of ln

SL 5.6

f(x)=lnx⇒f′(x)=x1📖

Product and Quotient rule

SL 5.6

The product and quotient rules are given by

(uv)′=u′v+v′u📖

(vu)′=v2u′v−v′u📖

Derivatives of sin and cos

SL 5.6

f(x)=sinx⇒f′(x)=cosx📖

g(x)=cosx⇒g′(x)=−sinx📖