IB Maths AA SL 5.6 Differentiation Rules Questions

Practise differentiating powers, trigonometric, exponential and logarithmic functions with sum, chain, product and quotient rules.

Exam points

Differentiate x^n for rational n, sin x, cos x, e^x and ln x using sum and constant-multiple rules.
Apply the chain, product and quotient rules to composite or combined functions, simplifying the derivative and retaining domain restrictions.

[Maximum number: 3]

Let $f(x)=A \mathrm{e}^{k x}+3$ . Part of the graph of f is shown below.

Figure for Question IB Maths AA SL 5.6 Differentiation Rules Questions question 1 — IB Maths AA SL

The y-intercept is at (0,13).

Using your value of k, find $f^{\prime}(x)$ .

$\quad f(x)=10 \mathrm{e}^{-0.201 x}+3$ $f^{\prime}(x)=10 \mathrm{e}^{-0.201 x} \times-0.201 \quad\left(=-2.01 \mathrm{e}^{-0.201 x}\right)$
Note: Award A1 for $10 \mathrm{e}^{-0.201 x}, \boldsymbol{A} \mathbf{1}$ for x-0.201, A1 for the derivative of 3 is zero.

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IB Maths AA SL 5.6 Differentiation Rules Questions question 1