SL 5.3 & 5.6 The derivative of functions
Content
Derivative interpreted as gradient function and as rate of change.
Understandings:
- SL 5.3
- Derivative of f(x) = axn is f ′(x) = anxn−1 , n ∈ ℤ
- The derivative of functions of the form f(x) = axn + bxn−1 . . . . where all exponents are integers.
- SL 5.6
- Derivatives of \({x^n}\) , \(\sin x\) , \(\cos x\) , \(\tan x\) , \({{\text{e}}^x}\) and \(\ln x\) .
- Differentiation of a sum and a multiple of these functions.
- The chain rule for composite functions
- \(Example: f(x)=e^{(x^2+2)}, f(x)=sin(3x-1)\)
- The product and quotient rules
- Derivatives of \({x^n}\) , \(\sin x\) , \(\cos x\) , \(\tan x\) , \({{\text{e}}^x}\) and \(\ln x\) .
Guidance, clarification and syllabus links
- Link to: composite functions (SL2.5).