Advertisements
Advertisements
Question
If x = t.logt, y = tt, then show that `("d"y)/("d"x)` = tt
Advertisements
Solution
x = t.logt ......(i)
y = tt ......(ii)
Taking logarithm of both sides, we get
log y = log tt
∴ log y = t.logt
∴ log y = x ......[From (i)]
Differentiating both sides w.r.t. x, we get
`1/y*("d"y)/("d"x)` = 1
∴ `("d"y)/("d"x)` = y
∴ `("d"y)/("d"x)` = tt ......[From (ii)]
APPEARS IN
RELATED QUESTIONS
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")`
If y = x log x, then `(d^2y)/dx^2`= ______.
The derivative of ax is ax log a.
Solve the following:
If y = [log(log(logx))]2, find `"dy"/"dx"`
Choose the correct alternative:
If y = (x )x + (10)x, then `("d"y)/("d"x)` = ?
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 xy = log(xy)
Find `("d"y)/("d"x)`, if x = `sqrt(1 + "u"^2)`, y = log(1 +u2)
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`
If y = (log x)2 the `dy/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^(e^x)`
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^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", y = x^(e^(x))`
