Advertisements
Advertisements
प्रश्न
`2^(cos^(2_x)`
Advertisements
उत्तर
Let y = `2^(cos^(2_x)`
Taking log on both sides, we get
log y = `log 2^(cos^(2_x)`
⇒ log y = `cos^2x * log 2`
Differentiating both sides w.r.t. x
⇒ `1/y * "dy"/"dx" = log 2* "d"/"dx" cos^2x`
⇒ `1/y * "dy"/"dx" = log 2 [2 cos x * "d"/"dx" cos x]`
⇒ `1/y * "dy"/"dx" = log 2 [2 cos x(-sin x)]`
⇒ `1/y * "dy"/"dx" = log 2 (- sin 2x)`
`"dy"/"dx" = - y * log 2 sin 2x`
Hence, `"dy"/"dx" = -2^(cos^2x) (log 2 sin 2x)`
APPEARS IN
संबंधित प्रश्न
If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`
if xx+xy+yx=ab, then find `dy/dx`.
Differentiate the function with respect to x.
(log x)x + xlog x
Differentiate the function with respect to x.
`(sin x)^x + sin^(-1) sqrtx`
Differentiate the function with respect to x.
xsin x + (sin x)cos x
Find `bb(dy/dx)` for the given function:
xy = `e^((x - y))`
Find the derivative of the function given by f(x) = (1 + x) (1 + x2) (1 + x4) (1 + x8) and hence find f′(1).
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`
If ey ( x +1) = 1, then show that `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`
Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`
`"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 = esin3t, y = ecos3t, then show that `dy/dx = -(ylogx)/(xlogy)`.
Find the second order derivatives of the following : x3.logx
If y = log (log 2x), show that xy2 + y1 (1 + xy1) = 0.
Find the nth derivative of the following : log (2x + 3)
Choose the correct option from the given alternatives :
If xy = yx, then `"dy"/"dx"` = ..........
If y = log [cos(x5)] then find `("d"y)/("d"x)`
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.
If y = `{f(x)}^{phi(x)}`, then `dy/dx` is ______
If y = tan-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.
If y = `("e"^"2x" sin x)/(x cos x), "then" "dy"/"dx" = ?`
`log (x + sqrt(x^2 + "a"))`
If xm . yn = (x + y)m+n, prove that `"dy"/"dx" = y/x`
If y = `log ((1 - x^2)/(1 + x^2))`, then `"dy"/"dx"` is equal to ______.
`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)` is equal to ____________.
If `"y" = "e"^(1/2log (1 + "tan"^2"x")), "then" "dy"/"dx"` is equal to ____________.
If y = `x^(x^2)`, then `dy/dx` is equal to ______.
If y = `log(x + sqrt(x^2 + 4))`, show that `dy/dx = 1/sqrt(x^2 + 4)`
Find `dy/dx`, if y = (log x)x.
Evaluate:
`int log x dx`
