Advertisements
Advertisements
प्रश्न
Solve the following:
If y = [log(log(logx))]2, find `"dy"/"dx"`
Advertisements
उत्तर
y = [log(log(logx))]2
Differentiating both sides w.r.t. x, we get
`"dy"/"dx" = "d"/"dx" [log(log(log "x"))]^2`
`= 2[log(log(log "x"))] xx "d"/"dx" [log(log(log "x"))]`
`= 2[log(log(log "x"))] xx 1/(log(log "x")) xx "d"/"dx" [log(log "x")]`
`= 2[log(log(log "x"))] xx 1/(log(log "x")) xx 1/(log "x") xx "d"/"dx" (log "x")`
`= 2[log(log(log "x"))] xx 1/(log(log "x")) xx 1/(log "x") xx 1/"x"`
∴ `"dy"/"dx" = (2[log(log(log "x"))])/("x"(log "x")(log (log "x")))`
Notes
The answer in the textbook is incorrect.
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `"x"^("x"^"2x")`
Find `"dy"/"dx"`if, y = (2x + 5)x
Find `"dy"/"dx"`if, y = `root(3)(("3x" - 1)/(("2x + 3")(5 - "x")^2))`
Find `"dy"/"dx"`if, y = `(log "x"^"x") + "x"^(log "x")`
Find `dy/dx`if, y = `(x)^x + (a^x)`.
Find `"dy"/"dx"`if, y = `10^("x"^"x") + 10^("x"^10) + 10^(10^"x")`
Fill in the blank.
If x = t log t and y = tt, then `"dy"/"dx"` = ____
If y = x log x, then `(d^2y)/dx^2`= ______.
State whether the following is True or False:
If y = e2, then `"dy"/"dx" = 2"e"`
Find `"dy"/"dx"` if y = `sqrt(((3"x" - 4)^3)/(("x + 1")^4("x + 2")))`
Differentiate log (1 + x2) with respect to ax.
If u = 5x and v = log x, then `("du")/("dv")` is ______
State whether the following statement is True or False:
If y = log(log x), then `("d"y)/("d"x)` = logx
State whether the following statement is True or False:
If y = 4x, then `("d"y)/("d"x)` = 4x
Find `("d"y)/("d"x)`, if y = [log(log(logx))]2
Find `("d"y)/("d"x)`, if x = `sqrt(1 + "u"^2)`, y = log(1 +u2)
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)`
Find `("d"y)/("d"x)`, if y = `root(3)(((3x - 1))/((2x + 3)(5 - x)^2)`
`int 1/(4x^2 - 1) dx` = ______.
Find`dy/dx if, y = x^(e^x)`
FInd `dy/dx` if,`x=e^(3t), y=e^sqrtt`
Find `dy/dx` if, y = `x^(e^x)`
Find `dy/dx,"if" y=x^x+(logx)^x`
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`.
