IB Maths AA HL Sl 5 3 Derivative of Powers Questions

Practise differentiating integer powers and sums of power terms, identifying the correct derivative rule and checking the resulting function or rate of change.

Exam points

Differentiate f(x) = ax^n for integer n using f′(x) = anx^(n−1), including negative and zero powers where defined.
Differentiate sums of integer-power terms term-by-term and simplify the resulting derivative for use in a stated problem.

[Maximum number: 4]

Consider the function $f(x)=a x^{3}+b x^{2}+c x+d$ , where $x \in \mathbb{R}$ and $a, b, c, d \in \mathbb{R}$ .

Write down an expression for $f^{\prime}(x)$ .

$f^{\prime}(x)=3 a x^{2}+2 b x+c \quad \boldsymbol{A} \mathbf{1}$

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IB Maths AA HL Sl 5 3 Derivative of Powers Questions question 1