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

Apply the chain, product and quotient rules to differentiate composite, product and quotient functions, including exponential, logarithmic and trigonometric forms.
Evaluate derivatives at specified inputs and interpret them as gradients, rates of change, population growth, velocity or acceleration.
Use first and second derivatives to solve stationary-point, horizontal-tangent, maximum-rate and parameter problems.

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Study SL 5.6—Differentiation rules conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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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