Differentiation rules

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

AHL AI 5.9

f(x)=xn, n∈Q⇒f′(x)=nxn−1📖

Chain rule

AHL AI 5.9

(g(f(x)))′=g′(f(x))⋅f′(x)🚫

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

dxdy=dudg⋅dxdu📖

Derivative of e^x

AHL AI 5.9

f(x)=ex⇒f′(x)=ex📖

Derivative of ln

AHL AI 5.9

f(x)=lnx⇒f′(x)=x1📖

Product and Quotient rule

AHL AI 5.9

The product and quotient rules are given by

(uv)′=u′v+v′u📖

(vu)′=v2u′v−v′u📖

Derivatives of sin and cos

AHL AI 5.9

f(x)=sinx⇒f′(x)=cosx📖

g(x)=cosx⇒g′(x)=−sinx📖

Derivative of tan(x)

AHL AI 5.9

f(x)=tanx⇒f′(x)=sec2(x)📖

Exercises

Key Skills

Derivative of xⁿ where n is an integer

Derivatives of sums and scalar multiples

Derivative of xⁿ where n is rational

Chain rule

Derivative of e^x

Derivative of ln

Product and Quotient rule

Derivatives of sin and cos

Derivative of tan(x)

Derivative of xⁿ where n is an integer

Derivatives of sums and scalar multiples

Derivative of xⁿ where n is rational

Chain rule

Derivative of e^x

Derivative of ln

Product and Quotient rule

Derivatives of sin and cos

Derivative of tan(x)