Advertisements
Advertisements
Question
Solve the following:
If y = [log(log(logx))]2, find `"dy"/"dx"`
Solution
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
RELATED QUESTIONS
Find `"dy"/"dx"`if, y = `"e"^("x"^"x")`
If y = log `("e"^"x"/"x"^2)`, then `"dy"/"dx" = ?`
Fill in the Blank
If 0 = log(xy) + a, then `"dy"/"dx" = (-"y")/square`
Fill in the blank.
If x = t log t and y = tt, then `"dy"/"dx"` = ____
State whether the following is True or False:
The derivative of `log_ax`, where a is constant is `1/(x.loga)`.
State whether the following is True or False:
If y = log x, then `"dy"/"dx" = 1/"x"`
Find `"dy"/"dx"` if y = `sqrt(((3"x" - 4)^3)/(("x + 1")^4("x + 2")))`
If y = `"a"^((1 + log"x"))`, then `("d"y)/("d"x)` is ______
If x = t.logt, y = tt, then show that `("d"y)/("d"x)` = tt
Find `("d"y)/("d"x)`, if y = (log x)x + (x)logx
If xa .yb = `(x + y)^((a + b))`, then show that `("d"y)/("d"x) = y/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 = e^(x+y)`
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", y = x^(e^x)`
Find `dy/(dx)` if, `x = e^(3t), y = e^sqrtt`.
