Advertisements
Advertisements
प्रश्न
If `sin^-1((x^5 - y^5)/(x^5 + y^5)) = pi/(6), "show that" "dy"/"dx" = x^4/(3y^4)`
Advertisements
उत्तर
`sin^-1((x^5 - y^5)/(x^5 + y^5)) = pi/(6)`
∴ `(x^5 - y^5)/(x^5 + y^5) = sin pi/(6) = (1)/(2)`
∴ 2x5 – 2y5 = x5 + y5
∴ 3y5 = x5
Differentiating both sides w.r.t. x, we get
`3 xx 5y^4"dy"/"dx"` = 5x4
∴ `"dy"/"dx" = x^4/(3y^4)`.
APPEARS IN
संबंधित प्रश्न
If y=eax ,show that `xdy/dx=ylogy`
Find `bb(dy/dx)` in the following:
x2 + xy + y2 = 100
Find `bb(dy/dx)` in the following:
sin2 y + cos xy = k
if `x^y + y^x = a^b`then Find `dy/dx`
Write the derivative of f (x) = |x|3 at x = 0.
If \[\lim_{x \to c} \frac{f\left( x \right) - f\left( c \right)}{x - c}\] exists finitely, write the value of \[\lim_{x \to c} f\left( x \right)\]
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 = sinθ, y = tanθ
Find `"dy"/"dx"` if : x = t2 + t + 1, y = `sin((pit)/2) + cos((pit)/2) "at" t = 1`
Differentiate `tan^-1((cosx)/(1 + sinx)) w.r.t. sec^-1 x.`
Differentiate xx w.r.t. xsix.
Differentiate `tan^-1((sqrt(1 + x^2) - 1)/(x)) w.r.t tan^-1((2xsqrt(1 - x^2))/(1 - 2x^2))`.
Find `(d^2y)/(dx^2)` of the following : x = a(θ – sin θ), y = a(1 – cos θ)
Find `(d^2y)/(dx^2)` of the following : x = sinθ, y = sin3θ at θ = `pi/(2)`
If `sec^-1((7x^3 - 5y^3)/(7^3 + 5y^3)) = "m", "show" (d^2y)/(dx^2)` = 0.
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 : cos x
Find the nth derivative of the following : y = eax . cos (bx + c)
Choose the correct option from the given alternatives :
Let `f(1) = 3, f'(1) = -(1)/(3), g(1) = -4 and g'(1) =-(8)/(3).` The derivative of `sqrt([f(x)]^2 + [g(x)]^2` w.r.t. x at x = 1 is
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)?
Choose the correct option from the given alternatives :
If y = `tan^-1(x/(1 + sqrt(1 - x^2))) + sin[2tan^-1(sqrt((1 - x)/(1 + x)))] "then" "dy"/"dx"` = ...........
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?
Differentiate the following w.r.t. x : `sin[2tan^-1(sqrt((1 - x)/(1 + x)))]`
Differentiate the following w.r.t. x : `sin^2[cot^-1(sqrt((1 + x)/(1 - x)))]`
Differentiate the following w.r.t. x : `tan^-1((sqrt(x)(3 - x))/(1 - 3x))`
If log y = log (sin x) – x2, show that `(d^2y)/(dx^2) + 4x "dy"/"dx" + (4x^2 + 3)y` = 0.
If `"x"^5 * "y"^7 = ("x + y")^12` then show that, `"dy"/"dx" = "y"/"x"`
If log (x + y) = log (xy) + a then show that, `"dy"/"dx" = (- "y"^2)/"x"^2`.
Choose the correct alternative.
If y = 5x . x5, then `"dy"/"dx" = ?`
If y = `("x" + sqrt("x"^2 - 1))^"m"`, then `("x"^2 - 1) "dy"/"dx"` = ______.
If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`
If x = a t4 y = 2a t2 then `("d"y)/("d"x)` = ______
If y = `sqrt(tansqrt(x)`, find `("d"y)/("d"x)`.
If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______
Find `(dy)/(dx)` if x + sin(x + y) = y – cos(x – y)
If `tan ((x + y)/(x - y))` = k, then `dy/dx` is equal to ______.
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
If log (x+y) = log (xy) + a then show that, `dy/dx= (-y^2)/(x^2)`
If y = `(x + sqrt(x^2 - 1))^m`, show that `(x^2 - 1)(d^2y)/(dx^2) + xdy/dx` = m2y
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`
