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Question
Differentiate the following with respect to x.
(ax2 + bx + c)n
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Solution
For the following problems chain rule to be used:
`"d"/"dx"` f(g(x)) = f'(g(x)) . g'(x)
`"d"/"dx"` [f(x)]n = n[f(x)]n-1 × `"d"/"dx"`f(x)
Let y = (ax2 + bx + c)n
`"dy"/"dx"= "n"("a"x^2 + "b"x + "c")^("n"-1) "d"/"dx" ("a"x^2 + "b"x + "c")`
= n(ax2 + bx + c)n-1 (2ax + b)
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