Advertisement Remove all ads

Find dy/dx if y = x^e^x - Mathematics and Statistics

Sum

Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`

Advertisement Remove all ads

Solution

y = `"x"^("e"^"x")`

Taking logarithm of both sides, we get

log y = log `"x"^("e"^"x") = "e"^"x" log "x"`

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

`1/"y" * "dy"/"dx" = "e"^"x" "d"/"dx" (log "x") + log "x" "d"/"dx" ("e"^"x")`

`= "e"^"x" xx 1/"x" + (log "x")"e"^"x"`

∴ `"dy"/"dx" = "y" * "e"^"x"(1/"x" + log "x") = "x"^("e"^"x") "e"^"x"(1/"x" + log "x")`

Concept: Derivative - Derivatives of Logarithmic Functions
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×