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IB Maths AI SL 5.3 Derivative of powers

IB Maths AI SL 5.3 Derivative of powers
IB Mathematics: applications and interpretation guide, first assessment 2021

Students practise differentiating algebraic functions—including negative and fractional powers—using the power rule, often as a step toward optimisation or interpretation.

How this is tested

  • differentiate B(x) = 32/x + 2x to obtain B′(x) = −32x⁻² + 2, correctly handling x⁻¹ terms
  • differentiate a negative power of a rational expression and simplify
  • differentiate the area function term by term and relate each derivative

Question 11(a)(i)

[Maximum number: 6]

Consider the function B(x)=20+32x+2xB(x)=20+\frac{32}{x}+2 x, where x≥1,x∈Rx \geq 1, x \in \mathbb{R}.

Find B′(x)B^{\prime}(x).