Advertisements
Advertisements
प्रश्न
Find `bb(dy/dx)` in the following:
ax + by2 = cos y
Advertisements
उत्तर
ax + by2 = cos y
Differentiating both sides with respect to x,
⇒ `a d/dx (x) + b d/dx (y^2) = d/dx(cos y)`
⇒ `a xx 1 + b * 2y dy/dx = - sin y dy/dx`
⇒ `a + 2by dy/dx + sin y dy/dx = 0`
⇒ `a + dy/dx (2by +sin y) = 0`
⇒ `dy/dx (2by + sin y) = - a`
∴ `dy/dx = (-a)/(2by + sin y)`
APPEARS IN
संबंधित प्रश्न
Find dy/dx if x sin y + y sin x = 0.
Find `bb(dy/dx)` in the following:
x3 + x2y + xy2 + y3 = 81
if `x^y + y^x = a^b`then Find `dy/dx`
if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`
If \[f\left( x \right) = x^3 + 7 x^2 + 8x - 9\]
, find f'(4).
Is |sin x| differentiable? What about cos |x|?
Write the derivative of f (x) = |x|3 at x = 0.
Let \[f\left( x \right)\begin{cases}a x^2 + 1, & x > 1 \\ x + 1/2, & x \leq 1\end{cases}\] . Then, f (x) is derivable at x = 1, if
Find `"dy"/"dx"` ; if x = sin3θ , y = cos3θ
Find `(dy)/(dx) if y = cos^-1 (√x)`
If x = tan-1t and y = t3 , find `(dy)/(dx)`.
Find `"dy"/"dx"` if x = at2, y = 2at.
Find `"dy"/"dx"`, if : x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`
Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`
Find `"dy"/"dx"`, if : `x = cos^-1(4t^3 - 3t), y = tan^-1(sqrt(1 - t^2)/t)`.
Find `dy/dx` if : x = 2 cos t + cos 2t, y = 2 sin t – sin 2t at t = `pi/(4)`
DIfferentiate x sin x w.r.t. tan x.
Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`
Find `(d^2y)/(dx^2)` of the following : x = sinθ, y = sin3θ at θ = `pi/(2)`
Find the nth derivative of the following : eax+b
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 :
If y = `tan^-1(x/(1 + sqrt(1 - x^2))) + sin[2tan^-1(sqrt((1 - x)/(1 + x)))] "then" "dy"/"dx"` = ...........
Differentiate the following w.r.t. x : `sin[2tan^-1(sqrt((1 - x)/(1 + x)))]`
Differentiate the following w.r.t. x : `tan^-1[sqrt((sqrt(1 + x^2) + x)/(sqrt(1 + x^2) - x))]`
If log y = log (sin x) – x2, show that `(d^2y)/(dx^2) + 4x "dy"/"dx" + (4x^2 + 3)y` = 0.
If x= a cos θ, y = b sin θ, show that `a^2[y(d^2y)/(dx^2) + (dy/dx)^2] + b^2` = 0.
Find `"dy"/"dx" if, sqrt"x" + sqrt"y" = sqrt"a"`
Find `"dy"/"dx"` if, x3 + y3 + 4x3y = 0
Solve the following:
If `"e"^"x" + "e"^"y" = "e"^((x + y))` then show that, `"dy"/"dx" = - "e"^"y - x"`.
If x2 + y2 = 1, then `(d^2x)/(dy^2)` = ______.
If x2 + y2 = t + `1/"t"` and x4 + y4 = t2 + `1/"t"^2` then `("d"y)/("d"x)` = ______
`(dy)/(dx)` of `2x + 3y = sin x` is:-
y = `e^(x3)`
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`
Solve the following.
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`
