Question 1
Determine the derivative of \ (y = 5\ln(2x + 3)\) with respect to \ (x\).
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Mathematical Methods · Unit 3 · Differentiation of trigonometric functions and differentiation rules · Differentiation rules
Use the chain rule to determine the derivative of composite functions involving exponential, logarithmic and trigonometric functions, expressing derivatives in simplest and factorised form.
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Question 2
Determine the derivative with respect to x of the following function, expressing your answer in simplest factorised form. \( h(x) = \ln(\sin(3x) + 2) \cdot e^{2x} \)
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Question 3
Consider the function $h(x) = \ln(\sin(3x) + 4)$. (a) Use the chain rule to determine $h'(x)$, expressing your answer in simplest form. (2 marks) (b) Hence determine the exact value of $h'\left(\frac{\pi}{6}\right)$. (2 marks)
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Use the product rule to determine the derivative of exponential, logarithmic and trigonometric functions, expressing derivatives in simplest and factorised form.