Differentiating Other Functions (Edexcel IAL Maths)

Differentiating Other Functions (Trig, ln & e etc)

Spec point — 4.1

Differentiating other functions

How do I differentiate common functions?

• These are the common results

  • $\frac{d}{dx}(x^{n})=nx^{n-1}$
  • $\frac{d}{dx}(e^{x})=e^{x}$
  • $\frac{d}{dx}(a^{x})=a^{x}\mathrm{ln}a$ for $a>0$
  • $\frac{d}{dx}(\mathrm{ln}x)=\frac{1}{x}$
  • $\frac{d}{dx}(\mathrm{sin}x)=\mathrm{cos}x$
  • $\frac{d}{dx}(\mathrm{cos}x)=-\mathrm{sin}x$
  • $\frac{d}{dx}(\mathrm{tan}x)=\mathrm{sec}^{2}x$
  • $\frac{d}{dx}(\mathrm{cot}x)=-\mathrm{cos} \mathrm{ec}^{2}x$
  • $\frac{d}{dx}(\mathrm{sec}x)=\mathrm{sec}x\mathrm{tan}x$
  • $\frac{d}{dx}(\mathrm{cos} \mathrm{ec}x)=-\mathrm{cos} \mathrm{ec}x\mathrm{cot}x$

How do I differentiate e^kx, a^x, ln(kx) and a^kx?

• And for a^kx:

• This last formula can be derived from Formula 3 by using the chain rule

Exam Hint

• The formulae for some of these derivatives are not given in the formulae booklet – you need to know them.
• The formulae for e^kx and **ln x are the ones you absolutely do need to know .
• The other formulae can be derived from those two as shown above, and remember – the derivative of** ln kx is $\frac{1}{x}$, NOT $\frac{k}{x}$ !

Worked Example