Advertisements
Advertisements
प्रश्न
Find `bb(dy/dx)` in the following:
xy + y2 = tan x + y
Advertisements
उत्तर
xy + y2 = tan x + y
Differentiating both sides with respect to x,
⇒ `x d/dx (y) + y d/dx (x) + d/dx (y^2) = d/dx (tan x) + d/dx (y)`
⇒ `x dy/dx + y + 2y dy/dx = sec^2 x + dy/dx`
⇒ `dy/dx (x+ 2y - 1) = sec^2 x - y`
∴ `dy/dx = (sec^2 x - y)/(x + 2y - 1)`
APPEARS IN
संबंधित प्रश्न
Find `bb(dy/dx)` in the following:
ax + by2 = cos y
Find `bb(dy/dx)` in the following:
sin2 y + cos xy = k
Find `bb(dy/dx)` in the following:
sin2 x + cos2 y = 1
Show that the derivative of the function f given by
If \[f\left( x \right) = x^3 + 7 x^2 + 8x - 9\]
, find f'(4).
Find the derivative of the function f defined by f (x) = mx + c at x = 0.
Examine the differentialibilty of the function f defined by
\[f\left( x \right) = \begin{cases}2x + 3 & \text { if }- 3 \leq x \leq - 2 \\ \begin{array}xx + 1 \\ x + 2\end{array} & \begin{array} i\text { if } - 2 \leq x < 0 \\\text { if } 0 \leq x \leq 1\end{array}\end{cases}\]
If f (x) = |x − 2| write whether f' (2) exists or not.
Find `"dy"/"dx"` ; if x = sin3θ , y = cos3θ
Find `(dy)/(dx) , "If" x^3 + y^2 + xy = 10`
Differentiate tan-1 (cot 2x) w.r.t.x.
Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`
Find `dy/dx` if : x = 2 cos t + cos 2t, y = 2 sin t – sin 2t at t = `pi/(4)`
Find `"dy"/"dx"` if : x = t + 2sin (πt), y = 3t – cos (πt) at t = `(1)/(2)`
Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`
If x = cos t, y = emt, show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" - m^2y` = 0.
If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
If `sec^-1((7x^3 - 5y^3)/(7^3 + 5y^3)) = "m", "show" (d^2y)/(dx^2)` = 0.
Find the nth derivative of the following : eax+b
Choose the correct option from the given alternatives :
If x = a(cosθ + θ sinθ), y = a(sinθ – θ cosθ), then `((d^2y)/dx^2)_(θ = pi/4)` = .........
Solve the following :
f(x) = –x, for – 2 ≤ x < 0
= 2x, for 0 ≤ x < 2
= `(18 - x)/(4)`, for 2 < x ≤ 7
g(x) = 6 – 3x, for 0 ≤ x < 2
= `(2x - 4)/(3)`, for 2 < x ≤ 7
Let u (x) = f[g(x)], v(x) = g[f(x)] and w(x) = g[g(x)]. Find each derivative at x = 1, if it exists i.e. find u'(1), v' (1) and w'(1). If it doesn't exist, then explain why?
If `sqrt(y + x) + sqrt(y - x)` = c, show that `"dy"/"dx" = y/x - sqrt(y^2/x^2 - 1)`.
Choose the correct alternative.
If `"x"^4."y"^5 = ("x + y")^("m + 1")` then `"dy"/"dx" = "y"/"x"` then m = ?
Choose the correct alternative.
If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2` then `"dy"/"dx"` = ?
State whether the following is True or False:
The derivative of `"x"^"m"*"y"^"n" = ("x + y")^("m + n")` is `"x"/"y"`
If `"x"^"a"*"y"^"b" = ("x + y")^("a + b")`, then show that `"dy"/"dx" = "y"/"x"`
If x2 + y2 = 1, then `(d^2x)/(dy^2)` = ______.
If y = `sqrt(tansqrt(x)`, find `("d"y)/("d"x)`.
If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
`(dy)/(dx)` of `xy + y^2 = tan x + y` is
Find `(d^2y)/(dy^2)`, if y = e4x
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 ______.
Find `dy/dx if , x = e^(3t) , y = e^sqrtt`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
Find `dy/dx"if", x= e^(3t), y=e^sqrtt`
Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
