Advertisements
Advertisements
प्रश्न
Find `(dy)/(dx)`, if xy = yx
Advertisements
उत्तर
Given xy = yx
Taking logarithm of both sides, we get
log xy = log yx
∴ y log x = x log y
Differentiating both sides w.r.t.x, we get
`d/(dx)(ylogx) = d/(dx)(xlogy)`
∴ `y.d/(dx)(logx) + d/(dx)(y) = x.d/(dx)(logy) + logy. d/(dx)(x)`
∴ `y. 1/x + logx.(dy)/(dx) = x. 1/y.(dy)/(dx) + logy.1`
∴ `(logx - x/y)(dy)/(dx) = (logy - y/x)`
∴ `((ylogx - x)/y) (dy)/(dx) = (xlogy - y)/x`
∴ `(dy)/(dx) = ((xlogy - y)/x) xx (y/(ylogx - x))`
∴ `(dy)/(dx) = y/x((xlogy - y)/(ylogx - x))`
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `"e"^("x"^"x")`
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 = `(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 0 = log(xy) + a, then `"dy"/"dx" = (-"y")/square`
If y = x log x, then `(d^2y)/dx^2`= ______.
If y = `"e"^"ax"`, then `"x" * "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 = e2, then `"dy"/"dx" = 2"e"`
Differentiate log (1 + x2) with respect to ax.
If u = ex and v = loge 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
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
Solve the following differential equations:
x2ydx – (x3 – y3)dy = 0
`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=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))`
