Advertisements
Advertisements
प्रश्न
If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`
Advertisements
उत्तर
`(sin "x")^"y" = "x" + "y"`
Take log on both the sides,
`log(sin "x")^"y" = log("x" + "y")`
⇒ `"y" log (sin "x") = log ("x" + "y")` ......(i)
Differentiate (i) w.r.t.x
`log (sin "x")· (d"y")/(d"x") + "y"· (d)/(d"x") [ log(sin "x")] = (d)/(d"x") [log ("x"+"y") ]`
⇒ `log (sin "x")· (d"y")/(d"x") + "y"· (cos "x")/(sin"x") = (1)/(("x"+"y"))· (1+ (d"y")/(d"x"))`
⇒ `(d"y")/(d"x") [ log( sin "x") - (1)/(("x"+"y"))] = (1)/(("x"+"y")) - "y"·cot "x" `
⇒ `(d"y")/(d"x") = (1 - ("xy" + "y"^2)·cot "x")/(("x"+"y")·log (sin "x") -1)`
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
xx − 2sin x
Differentiate the function with respect to x.
(x + 3)2 . (x + 4)3 . (x + 5)4
Differentiate the function with respect to x.
`(sin x)^x + sin^(-1) sqrtx`
Find the derivative of the function given by f(x) = (1 + x) (1 + x2) (1 + x4) (1 + x8) and hence find f′(1).
If x = a (cos t + t sin t) and y = a (sin t – t cos t), find `(d^2y)/dx^2`.
If y = `e^(acos^(-1)x)`, −1 ≤ x ≤ 1, show that `(1- x^2) (d^2y)/(dx^2) -x dy/dx - a^2y = 0`.
if `x^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`
Find `"dy"/"dx"` if y = xx + 5x
If y = (log x)x + xlog x, find `"dy"/"dx".`
If x = `asqrt(secθ - tanθ), y = asqrt(secθ + tanθ), "then show that" "dy"/"dx" = -y/x`.
Find the second order derivatives of the following : x3.logx
Find the second order derivatives of the following : log(logx)
Find the nth derivative of the following : log (2x + 3)
If y = A cos (log x) + B sin (log x), show that x2y2 + xy1 + y = 0.
If f(x) = logx (log x) then f'(e) is ______
If y = `log[sqrt((1 - cos((3x)/2))/(1 +cos((3x)/2)))]`, find `("d"y)/("d"x)`
If y = 5x. x5. xx. 55 , find `("d"y)/("d"x)`
lf y = `2^(x^(2^(x^(...∞))))`, then x(1 - y logx logy)`dy/dx` = ______
If xy = ex-y, then `"dy"/"dx"` at x = 1 is ______.
If y = tan-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.
`8^x/x^8`
`log [log(logx^5)]`
If `"f" ("x") = sqrt (1 + "cos"^2 ("x"^2)), "then the value of f'" (sqrtpi/2)` is ____________.
If y = `(1 + 1/x)^x` then `(2sqrt(y_2(2) + 1/8))/((log 3/2 - 1/3))` is equal to ______.
If y = `x^(x^2)`, then `dy/dx` is equal to ______.
If `log_10 ((x^3 - y^3)/(x^3 + y^3))` = 2 then `dy/dx` = ______.
If `log_10 ((x^2 - y^2)/(x^2 + y^2))` = 2, then `dy/dx` is equal to ______.
Find `dy/dx`, if y = (sin x)tan x – xlog x.
The derivative of log x with respect to `1/x` is ______.
