# Find dydxif, y = (2x + 5)x - Mathematics and Statistics

Sum

Find "dy"/"dx"if, y = (2x + 5)x

#### Solution

y = (2x + 5)x

Taking logarithm of both sides, we get

log y = log (2x + 5)x

∴ log y = x * log (2x + 5)

Differentiating both sides w.r.t.x, we get

1/"y" "dy"/"dx" = "x" * "d"/"dx"[log (2"x" + 5)] + log ("2x" + 5) * "d"/"dx" ("x")

= "x" * 1/("2x" + 5) * "d"/"dx" ("2x" + 5) + log (2"x" + 5) * (1)

= "x"/("2x" + 5) * (2 + 0) + log (2"x" + 5)

∴ 1/"y" "dy"/"dx" = "2x"/("2x" + 5) + log ("2x" + 5)

∴ "dy"/"dx" = "y"["2x"/("2x" + 5) + log ("2x" + 5)]

∴ "dy"/"dx" = ("2x" + 5)^"x" [log ("2x" + 5) + "2x"/("2x" + 5)]

Concept: Derivative - Derivatives of Logarithmic Functions
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