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# Calculus - Differentiation of the Function

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1. If f(theta) = 10sin^2 (0.4 theta - 0.1) show that f'(theta) = 4 sin (0.8 theta - 0.2)
and evaluate f" (pi / 4) correct to 3 decimal places

2. Differentiate the following functions:
i. f (t) = (3t-2) sin 2t
ii. f (theta) = 2 cos(3 theta - 1) / 3 theta

##### Solution Summary

This solution contains step-by-step calculations to prove and differentiate specific functions.

##### Solution Preview

(1) f(theta) = 10 sin^2 (0.4 theta - 0.1)

Differentiating with respect to theta using chain rule, we get

f'(theta) = 10 [2 sin(0.4 theta - 0.1)] cos(0.4 theta - 0.1) (0.4) = 4 [2 sin(0.4 theta - ...

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