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1.9.14 Chain rule (A-level only)

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Question 40
i.

Determine ddxln⁡(sec⁡43x)\frac{d}{dx}\ln(\sec^4 3x)dxd​ln(sec43x), giving your answer in its simplest form.

[3]
iia.

Differentiate (3x2−4)3(3x^2 - 4)^3(3x2−4)3 with respect to xxx.

[2]
iib.

Hence show that

∫02x(3x2−4)2 dx=K \int_{0}^{2} x(3x^2 - 4)^2 \, dx = K ∫02​x(3x2−4)2dx=K

where KKK is an integer to be found.

(Solutions relying on calculator technology are not acceptable.)

[4]

1.9.14 Chain rule (A-level only) Questions

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