Advertisements
Advertisements
प्रश्न
Find `dy/dx` in the following:
sin2 y + cos xy = k
उत्तर
Since, sin2 y + cos xy = k
Differentiating both sides with respect to x,
`d/dx (sin^2 y) + d/dx (cos xy) = d/dx (k)`
`=> 2 sin y cos y dy/dx + (- sin xy) d/dx (xy) = 0`
`=> 2 sin y cos y dy/dx - sin xy [x dy/dx + y d/dx (x)] = 0`
`=> 2 sin y cos y dy/dx - x sin xy dy/dx - y sin xy = 0`
`=> sin 2y - x sin xy dy/dx - y sin xy = 0`
`=> dy/dx (sin 2y - x sin xy) = y sin xy`
`dy/dx = (y sin xy)/((sin 2y - x sin xy))`
APPEARS IN
संबंधित प्रश्न
Find `dy/dx` in the following.
x3 + x2y + xy2 + y3 = 81
If for the function
\[\Phi \left( x \right) = \lambda x^2 + 7x - 4, \Phi'\left( 5 \right) = 97, \text { find } \lambda .\]
If f (x) = |x − 2| write whether f' (2) exists or not.
Write the derivative of f (x) = |x|3 at x = 0.
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Find `"dy"/"dx"` ; if y = cos-1 `("2x" sqrt (1 - "x"^2))`
Differentiate e4x + 5 w.r..t.e3x
Find `(dy)/(dx) , "If" x^3 + y^2 + xy = 10`
Find `(dy)/(dx) if y = cos^-1 (√x)`
Find `"dy"/"dx"`, if : x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`
Find `dy/dx` if : x = 2 cos t + cos 2t, y = 2 sin t – sin 2t at t = `pi/(4)`
If x = `(t + 1)/(t - 1), y = (t - 1)/(t + 1), "then show that" y^2 + "dy"/"dx"` = 0.
Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`
Differentiate `tan^-1((cosx)/(1 + sinx)) w.r.t. sec^-1 x.`
If x2 + 6xy + y2 = 10, show that `(d^2y)/(dx^2) = (80)/(3x + y)^3`.
If x = a sin t – b cos t, y = a cos t + b sin t, show that `(d^2y)/(dx^2) = -(x^2 + y^2)/(y^3)`.
Find the nth derivative of the following:
`(1)/x`
Find the nth derivative of the following : eax+b
Find the nth derivative of the following : sin (ax + b)
Choose the correct option from the given alternatives :
If f(x) = `sin^-1((4^(x + 1/2))/(1 + 2^(4x)))`, which of the following is not the derivative of f(x)?
Suppose that the functions f and g and their derivatives with respect to x have the following values at x = 0 and x = 1:
| x | f(x) | g(x) | f')x) | g'(x) |
| 0 | 1 | 5 | `(1)/(3)` | |
| 1 | 3 | – 4 | `-(1)/(3)` | `-(8)/(3)` |
(i) The derivative of f[g(x)] w.r.t. x at x = 0 is ......
(ii) The derivative of g[f(x)] w.r.t. x at x = 0 is ......
(iii) The value of `["d"/"dx"[x^(10) + f(x)]^(-2)]_(x = 1_` is ........
(iv) The derivative of f[(x + g(x))] w.r.t. x at x = 0 is ...
Differentiate the following w.r.t. x:
`tan^-1(x/(1 + 6x^2)) + cot^-1((1 - 10x^2)/(7x))`
If `sqrt(y + x) + sqrt(y - x)` = c, show that `"dy"/"dx" = y/x - sqrt(y^2/x^2 - 1)`.
If x sin (a + y) + sin a . cos (a + y) = 0, then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
Differentiate `tan^-1((sqrt(1 + x^2) - 1)/x)` w.r.t. `cos^-1(sqrt((1 + sqrt(1 + x^2))/(2sqrt(1 + x^2))))`
Find `"dy"/"dx" if, sqrt"x" + sqrt"y" = sqrt"a"`
Find `"dy"/"dx"` if, yex + xey = 1
Choose the correct alternative.
If `"x"^4."y"^5 = ("x + y")^("m + 1")` then `"dy"/"dx" = "y"/"x"` then m = ?
If y = `("x" + sqrt("x"^2 - 1))^"m"`, then `("x"^2 - 1) "dy"/"dx"` = ______.
If x2 + y2 = 1, then `(d^2x)/(dy^2)` = ______.
Find `(d^2y)/(dy^2)`, if y = e4x
If y = y(x) is an implicit function of x such that loge(x + y) = 4xy, then `(d^2y)/(dx^2)` at x = 0 is equal to ______.
Let y = y(x) be a function of x satisfying `ysqrt(1 - x^2) = k - xsqrt(1 - y^2)` where k is a constant and `y(1/2) = -1/4`. Then `(dy)/(dx)` at x = `1/2`, is equal to ______.
If y = `sqrt(tan x + sqrt(tanx + sqrt(tanx + .... + ∞)`, then show that `dy/dx = (sec^2x)/(2y - 1)`.
Find `dy/dx` at x = 0.
If log (x + y) = log (xy) + a then show that, `dy/dx = (−y^2)/x^ 2`
Find `dy/dx` if, x = e3t, y = `e^sqrtt`
Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`
Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`
