Given y = x(2x + 1)^{4}, show that \frac{dy}{dx} = (2x + 1)^{n}(Ax + B)
where n, A and B are constants to be found. - Edexcel - A-Level Maths Pure - Question 5 - 2017 - Paper 2
Question 5
Given y = x(2x + 1)^{4}, show that \frac{dy}{dx} = (2x + 1)^{n}(Ax + B)
where n, A and B are constants to be found.
Worked Solution & Example Answer:Given y = x(2x + 1)^{4}, show that \frac{dy}{dx} = (2x + 1)^{n}(Ax + B)
where n, A and B are constants to be found. - Edexcel - A-Level Maths Pure - Question 5 - 2017 - Paper 2
Step 1
Attempt to differentiate using the product rule
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Answer
To find \frac{dy}{dx}, we will use the product rule and chain rule. Let \ u = x \ and \ v = (2x + 1)^{4}.
Then, applying the product rule, we get:
[ \frac{dy}{dx} = \frac{du}{dx} v + u \frac{dv}{dx} ]
Here, \frac{du}{dx} = 1 \ and \ v = (2x + 1)^{4}.
Step 2
Differentiate \ v
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Answer
Next, we need to differentiate \v = (2x + 1)^{4}\ using the chain rule:
