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Differentiate $y=(x^2-3x)^4\cdot\cos x$ with respect to $x$
in A Level Maths by Diamond (49,546 points) | 22 views

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I am afraid that Nyasha Midzi's answer is incorrect. We area all human and so we all make mistakes. I can only hope that my mistakes are rare enough that I do my more good than harm with my answers.

Anyway, the answer is in the pic below. I have also given some commentary below the picture.

Please note that cos(x) means "cos of x" or "cos with x as it's input" NOT "cos*x". Also take note that some text and steps are only there for illustrative purposes.

We start by selecting f(x) and g(x). Then we use the product rule. Then we use the chain rule.

Personally, I find that in general the use of brackets helps to reduce the number of mistakes I make. They also help to clarify and illustrate Mathematical workings. Thus I have been somewhat heavy on my use of them here.

I will note that perhaps I should have put in more explanation of the chain rule.

 

by Wooden (162 points)
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dy/dx = 4(x^2-3x)^3 (2x -3) -sinx (x^2-3x)^4 = (8x-12) (x^2-3x)^3 - sin x (x^2-3x)^4
by Bronze Status (5,245 points)

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