Advertisements
Advertisements
प्रश्न
The derivative of x2x w.r.t. x is ______.
विकल्प
x2x – 1
2x2x log x
2x2x (1 + log x)
2x2x (1 – log x)
Advertisements
उत्तर
The derivative of x2x w.r.t. x is 2x2x (1 + log x).
Explanation:
Let y = x2x
log y = 2x log x ...(Taking log on both sides)
Differentiating w.r.t. x,
`1/y dy/dx` = 2[1 + log x]
`\implies dy/dx` = 2x2x [1 + log x]
संबंधित प्रश्न
Differentiate the following function with respect to x: `(log x)^x+x^(logx)`
If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`
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.
(log x)x + xlog x
Differentiate the function with respect to x.
`(x cos x)^x + (x sin x)^(1/x)`
Find `bb(dy/dx)` for the given function:
yx = xy
If cos y = x cos (a + y), with cos a ≠ ± 1, prove that `dy/dx = cos^2(a+y)/(sin a)`.
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 `y = sin^-1 x + cos^-1 x , "find" dy/dx`
Differentiate
log (1 + x2) w.r.t. tan-1 (x)
Find `"dy"/"dx"` , if `"y" = "x"^("e"^"x")`
If `"x"^(5/3) . "y"^(2/3) = ("x + y")^(7/3)` , the show that `"dy"/"dx" = "y"/"x"`
If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`
If `log_5((x^4 + y^4)/(x^4 - y^4)) = 2, "show that""dy"/"dx" = (12x^3)/(13y^3)`.
If xy = ex–y, then show that `"dy"/"dx" = logx/(1 + logx)^2`.
If y = `x^(x^(x^(.^(.^.∞))`, then show that `"dy"/"dx" = y^2/(x(1 - logy).`.
If ey = yx, then show that `"dy"/"dx" = (logy)^2/(log y - 1)`.
Find the nth derivative of the following: log (ax + b)
If f(x) = logx (log x) then f'(e) is ______
If y = `log[4^(2x)((x^2 + 5)/sqrt(2x^3 - 4))^(3/2)]`, find `("d"y)/("d"x)`
If xy = ex-y, then `"dy"/"dx"` at x = 1 is ______.
If y = tan-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.
If `("f"(x))/(log (sec x)) "dx"` = log(log sec x) + c, then f(x) = ______.
If y = `("e"^"2x" sin x)/(x cos x), "then" "dy"/"dx" = ?`
`log [log(logx^5)]`
Find `dy/dx`, if y = (log x)x.
If xy = yx, then find `dy/dx`
