IB Mathematics: Analysis and Approaches SL — Topic 5 Calculus
Power Rule Differentiation
Differentiate polynomial terms efficiently and connect the algebra to gradient.
AA SL · SL 5.3
Learning goal
Apply the power rule to polynomial functions with integer exponents.
Syllabus link
AA SL: SL 5.3 · Topic 5 Calculus.
Big idea
Differentiation changes both the coefficient and the power in a predictable way.
Key relationship
\(\frac{d}{dx}(ax^n)=anx^{n-1}\)
1
Core idea
Differentiation changes both the coefficient and the power in a predictable way.
Apply the power rule to polynomial functions with integer exponents.
2
Key results and method
\[\frac{d}{dx}(ax^n)=anx^{n-1}\]
\[\frac{d}{dx}(c)=0\]
- Multiply by the existing power.
- Reduce the power by 1.
- Differentiate each term separately and simplify.
3
Worked example
Question
Differentiate \(f(x)=4x^5-3x^2+7\).
Solution
- \(\frac{d}{dx}(4x^5)=20x^4\).
- \(\frac{d}{dx}(-3x^2)=-6x\).
- The constant differentiates to zero.
Answer: \(f\'(x)=20x^4-6x\).
4
Practice
Try these questions before moving on.
- Differentiate \(6x^4-5x+2\).
- Find the gradient of \(y=x^3-2x\) at \(x=2\).
- Find an equation for a curve whose derivative is \(6x^2\).
5
Tutorials and premium resources
Premium printable lesson notes
The finalized printable handout for this topic is a premium Radford Mathematics resource and is not offered as a free website download.
Visit the Radford Mathematics Store →