If y 2x 1 3 find frac dy dx - JAMB Mathematics 2010 Question
If y = (2x + 1)3, find \(\frac{dy}{dx}\)
A
6(2x + 1)
B
3(2x + 1)
C
6(2x + 1)2
D
2(2x + 1)2
correct option: c
If y = (2x + 1)3, then
Let u = 2x + 1 so that, y = u3
\(\frac{dy}{du}\) = 3u2 and \(\frac{dy}{dx}\) = 2
Hence by the chain rule,
\(\frac{dy}{dx}\) = \(\frac{dy}{du}\) x \(\frac{du}{dx}\)
= 3u2 x 2
= 6u2
= 6(2x + 1)2
Let u = 2x + 1 so that, y = u3
\(\frac{dy}{du}\) = 3u2 and \(\frac{dy}{dx}\) = 2
Hence by the chain rule,
\(\frac{dy}{dx}\) = \(\frac{dy}{du}\) x \(\frac{du}{dx}\)
= 3u2 x 2
= 6u2
= 6(2x + 1)2
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