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

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📖

Derivative of tan(x)

AHL 5.15

f(x)=tanx⇒f′(x)=sec2(x)📖

Derivatives of reciprocal trig functions

AHL 5.15

f(x)=secx⇒f′(x)=secxtanx📖

g(x)=cosecx⇒g′(x)=−cosecxcotx📖

h(x)=cotx⇒h′(x)=−cosec2(x)📖

Derivatives of inverse trig functions

AHL 5.15

f(x)=arcsinx⇒f′(x)=√1−x21📖

g(x)=arccosx⇒g′(x)=√1−x2−1📖

h(x)=arctanx⇒h′(x)=1+x21📖

Derivatives of aˣ and logₐ(x)

AHL 5.15

f(x)=ax⇒f′(x)=axlna📖

g(x)=logax⇒f′(x)=xlna1📖

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)

Derivatives of reciprocal trig functions

Derivatives of inverse trig functions

Derivatives of aˣ and logₐ(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)

Derivatives of reciprocal trig functions

Derivatives of inverse trig functions

Derivatives of aˣ and logₐ(x)