Advertisements
Advertisements
प्रश्न
Find `dy/dx`, if y = (log x)x.
Advertisements
उत्तर
y = (log x)x
Taking log of both sides,
log y = x log (logx)
Differentiating w.r.t. x,
`1/y dy/dx = x d/dx [log (log x)] + log (log x) d/dx (x)`
= `x * 1/(log x) * 1/x + log (log x) (1)`
`therefore dy/dx = y [1/(log x) + log (logx)]`
`therefore dy/dx = (log x)^x [1/(log x) + log (log x)]`
APPEARS IN
संबंधित प्रश्न
Differentiate the following function with respect to x: `(log x)^x+x^(logx)`
Differentiate the function with respect to x.
cos x . cos 2x . cos 3x
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.
`(x + 1/x)^x + x^((1+1/x))`
Differentiate the function with respect to x.
`x^(xcosx) + (x^2 + 1)/(x^2 -1)`
Find `bb(dy/dx)` for the given function:
yx = xy
Find `bb(dy/dx)` for the given function:
(cos x)y = (cos y)x
Differentiate (x2 – 5x + 8) (x3 + 7x + 9) in three ways mentioned below:
- By using the product rule.
- By expanding the product to obtain a single polynomial.
- By logarithmic differentiation.
Do they all give the same answer?
Differentiate the function with respect to x:
xx + xa + ax + aa, for some fixed a > 0 and x > 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")`
Differentiate : log (1 + x2) w.r.t. cot-1 x.
Find `"dy"/"dx"` if y = xx + 5x
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 (x + y) = log(xy) + p, where p is a constant, then prove that `"dy"/"dx" = (-y^2)/(x^2)`.
`"If" y = sqrt(logx + sqrt(log x + sqrt(log x + ... ∞))), "then show that" dy/dx = (1)/(x(2y - 1).`
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)`.
If x = log(1 + t2), y = t – tan–1t,show that `"dy"/"dx" = sqrt(e^x - 1)/(2)`.
If y = `log(x + sqrt(x^2 + a^2))^m`, show that `(x^2 + a^2)(d^2y)/(dx^2) + x "d"/"dx"` = 0.
If y = log (log 2x), show that xy2 + y1 (1 + xy1) = 0.
Find the nth derivative of the following: log (ax + b)
Choose the correct option from the given alternatives :
If xy = yx, then `"dy"/"dx"` = ..........
If y = A cos (log x) + B sin (log x), show that x2y2 + xy1 + y = 0.
If y = log [cos(x5)] then find `("d"y)/("d"x)`
If y = `log[sqrt((1 - cos((3x)/2))/(1 +cos((3x)/2)))]`, find `("d"y)/("d"x)`
If y = `(sin x)^sin x` , then `"dy"/"dx"` = ?
The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290 K and the metal temperature drops from 370 K to 330 K in 1 O min, then the time required to drop the temperature upto 295 K.
Derivative of loge2 (logx) with respect to x is _______.
Derivative of `log_6`x with respect 6x to is ______
`8^x/x^8`
If y = `log ((1 - x^2)/(1 + x^2))`, then `"dy"/"dx"` is equal to ______.
`lim_("x" -> 0)(1 - "cos x")/"x"^2` is equal to ____________.
If `"f" ("x") = sqrt (1 + "cos"^2 ("x"^2)), "then the value of f'" (sqrtpi/2)` is ____________.
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 ______.
If xy = yx, then find `dy/dx`
