Advertisements
Advertisements
प्रश्न
Find `("d"y)/("d"x)`, if xy = log(xy)
Advertisements
उत्तर
xy = log(xy)
Differentiating both sides w.r.t. x, we get
`x*("d"y)/("d"x) + y*"d"/("d"x)(x) = 1/(xy)*"d"/("d"x)(xy)`
∴ `x*("d"y)/("d"x) + y*1 = 1/(xy)[x*("d"y)/("d"x) + y*"d"/("d"x)(x)]`
∴ `x*("d"y)/("d"x) + y = 1/(xy)(x("d"y)/("d"x) + y*1)`
∴ `x*("d"y)/("d"x) + y = 1/y*("d"y)/("d"x) + 1/x`
∴ `(x - 1/y)("d"y)/("d"x) = 1/x - y`
∴ `-((1 - xy)/y)("d"y)/("d"x) = ((1 - xy)/x)`
∴ `("d"y)/("d"x) = -((1 - xy)/x) xx (y/(1 - xy))`
∴ `("d"y)/("d"x) = (-y)/x`
APPEARS IN
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 = `(log "x"^"x") + "x"^(log "x")`
If y = elogx then `dy/dx` = ?
If y = log `("e"^"x"/"x"^2)`, then `"dy"/"dx" = ?`
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`= ______.
Fill in the blank.
If y = y = [log (x)]2 then `("d"^2"y")/"dx"^2 =` _____.
The derivative of ax is ax log a.
Find `"dy"/"dx"` if y = `sqrt(((3"x" - 4)^3)/(("x + 1")^4("x + 2")))`
Choose the correct alternative:
If y = (x )x + (10)x, then `("d"y)/("d"x)` = ?
State whether the following statement is True or False:
If y = log(log x), then `("d"y)/("d"x)` = logx
Find `("d"y)/("d"x)`, if y = [log(log(logx))]2
Solve the following differential equations:
x2ydx – (x3 – y3)dy = 0
`int 1/(4x^2 - 1) dx` = ______.
If y = x . log x then `dy/dx` = ______.
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, `y = x^(e^x)`
