How do I differentiate a trigonometric function for something that is not just a single variable (e.g. d/dx (sin(3x))?

In order to differentiate a trig function with a term in front of the variable you are differentiating, you must use the chain rule. For example d/dx (sin (3x)) becomes 3cos(3x) because you have to multiply the two differentials: 3 and cos (3x).

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Answered by Kieran T. Maths tutor

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A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0 (a) Find (i) dy/d x (ii) d^2y/dx^2 (b) Verify that C has a stationary point when x = 4 (c) Determine the nature of this stationary point, giving a reason for your answer.


Use the chain rule to show that, if y = sec(x), then dy/dx = sec(x)tan(x).


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