Advertisements
Advertisements
Question
Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`
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")`
APPEARS IN
RELATED QUESTIONS
Find `dy/dx`if, y = `(x)^x + (a^x)`.
Find `"dy"/"dx"`if, y = `10^("x"^"x") + 10^("x"^10) + 10^(10^"x")`
If y = elogx then `dy/dx` = ?
Fill in the blank.
If y = y = [log (x)]2 then `("d"^2"y")/"dx"^2 =` _____.
Find `"dy"/"dx"` if y = `"x"^"x" + ("7x" - 1)^"x"`
Differentiate log (1 + x2) with respect to ax.
If y = `"a"^((1 + log"x"))`, then `("d"y)/("d"x)` is ______
If u = 5x and v = log x, then `("du")/("dv")` is ______
State whether the following statement is True or False:
If y = 4x, then `("d"y)/("d"x)` = 4x
If x = t.logt, y = tt, then show that `("d"y)/("d"x)` = tt
Find `("d"y)/("d"x)`, if y = xx + (7x – 1)x
Find `("d"y)/("d"x)`, if y = `x^(x^x)`
`int 1/(4x^2 - 1) dx` = ______.
Find `dy/dx , if y^x = e^(x+y)`
Find `dy/dx, "if" y=sqrt((2x+3)^5/((3x-1)^3(5x-2)))`
Find `dy/dx if, y = x^(e^x)`
Find `dy / dx` if, `y = x^(e^x)`
Find `dy/(dx) "if", y = x^(e^(x))`
Find `dy/(dx)` if, `x = e^(3t), y = e^sqrtt`.
