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Question
Choose the correct alternative.
If y = 5x . x5, then `"dy"/"dx" = ?`
Options
5x. x4 (5 + log 5)
5x. x5 (5 + log 5)
5x . x4 (5 + x log 5)
5x. x5 (5 + x log 5)
Solution
5x . x4 (5 + x log 5)
Explanation:
y = 5x . x5
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = 5^"x" * "d"/"dx" ("x"^5) + "x"^5 * "d"/"dx" (5^"x")`
`= 5^"x" * (5"x"^4) + "x"^5 (5^"x" * log 5)`
`= 5^"x" * "x"^4(5 + "x" log 5)`
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