Advertisements
Advertisements
Question
If sin−1(x3 + y3) = a then `("d"y)/("d"x)` = ______
Options
`(-x)/(cos"a")`
`(-x^2)/(y^2)`
`(y^2)/(x^2)`
`sin"a"/y`
Solution
`(-x^2)/(y^2)`
APPEARS IN
RELATED QUESTIONS
If y = eax. cos bx, then prove that
`(d^2y)/(dx^2) - 2ady/dx + (a^2 + b^2)y` = 0
Solve the following differential equation:
x2 dy + (xy + y2) dx = 0, when x = 1 and y = 1
Find `"dy"/"dx"` if `xsqrt(x) + ysqrt(y) = asqrt(a)`
Find `"dy"/"dx"` if xey + yex = 1
Find `"dy"/"dx"` if cos (xy) = x + y
Find `"dy"/"dx"` if, y = (5x3 - 4x2 - 8x)9
Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`
Choose the correct alternative.
If y = (5x3 - 4x2 - 8x)9, then `"dy"/"dx"` =
Choose the correct alternative.
If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
Solve the following:
If y = (6x3 - 3x2 - 9x)10, find `"dy"/"dx"`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25 + 30x – x2.
If y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x such that the composite function y = f[g(x)] is a differentiable function of x, then `("d"y)/("d"x) = ("d"y)/("d"u)*("d"u)/("d"x)`. Hence find `("d"y)/("d"x)` if y = sin2x
Suppose y = f(x) is a differentiable function of x on an interval I and y is one – one, onto and `("d"y)/("d"x)` ≠ 0 on I. Also if f–1(y) is differentiable on f(I), then `("d"x)/("d"y) = 1/(("d"y)/("d"x)), ("d"y)/("d"x)` ≠ 0
If y = `1/sqrt(3x^2 - 2x - 1)`, then `("d"y)/("d"x)` = ?
Choose the correct alternative:
If y = `root(3)((3x^2 + 8x - 6)^5`, then `("d"y)/("d"x)` = ?
Choose the correct alternative:
If y = `x^(sqrt(x))`, then `("d"y)/("d"x)` = ?
If y = x10, then `("d"y)/("d"x)` is ______
If y = `("e")^((2x + 5))`, then `("d"y)/("d"x)` is ______
If y = x2, then `("d"^2y)/("d"x^2)` is ______
State whether the following statement is True or False:
If y = ex, then `("d"y)/("d"x)` = ex
State whether the following statement is True or False:
If x2 + y2 = a2, then `("d"y)/("d"x)` = = 2x + 2y = 2a
Find `("d"y)/("d"x)`, if y = (6x3 – 3x2 – 9x)10
If u = x2 + y2 and x = s + 3t, y = 2s - t, then `(d^2u)/(ds^2)` = ______
If f(x) = `(x - 2)/(x + 2)`, then f(α x) = ______
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
Derivative of ex sin x w.r.t. e-x cos x is ______.
If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = ______.
Given f(x) = `1/(x - 1)`. Find the points of discontinuity of the composite function y = f[f(x)]
Differentiate `sqrt(tansqrt(x))` w.r.t. x
Find `("d"y)/("d"x)`, if y = `tan^-1 ((3x - x^3)/(1 - 3x^2)), -1/sqrt(3) < x < 1/sqrt(3)`
If y = `sin^-1 {xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)}` and 0 < x < 1, then find `("d"y)/(dx)`
If x = a sec3θ and y = a tan3θ, find `("d"y)/("d"x)` at θ = `pi/3`
If f(x) = |cos x|, find f'`((3pi)/4)`
If f(x) = |cos x – sinx|, find `"f'"(pi/6)`
If y = `sec^-1 ((sqrt(x) + 1)/(sqrt(x + 1))) + sin^-1((sqrt(x) - 1)/(sqrt(x) + 1))`, then `"dy"/"dx"` is equal to ______.
Differentiate the function from over no 15 to 20 sin (x2 + 5)
y = cos (sin x)
y = sin (ax+ b)
y = `2sqrt(cotx^2)`
y = `cos sqrt(x)`
If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.
If f(x) = `{{:(x^3 + 1",", x < 0),(x^2 + 1",", x ≥ 0):}`, g(x) = `{{:((x - 1)^(1//3)",", x < 1),((x - 1)^(1//2)",", x ≥ 1):}`, then (gof) (x) is equal to ______.
Find `"dy"/"dx" if, e ^(5"x"^2- 2"X"+4)`
Solve the following:
If`y=root(5)((3x^2+8x+5)^4),"find" (dy)/dx`
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
Find `dy/dx` if, y = `e^(5 x^2 - 2x + 4)`
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `dy/dx` if ,
`x= e^(3t) , y = e^(4t+5)`
lf y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, such that the composite function y = f[g(x)] is a differentiable function of x, then prove that:
`dy/dx = dy/(du) xx (du)/dx`
Hence, find `d/dx[log(x^5 + 4)]`.
Solve the following:
If y = `root5((3x^2 +8x+5)^4`,find `dy/dx`
Find `dy/dx` if, y = `e^(5x^2 -2x + 4)`
If y = `root5((3x^2 + 8x +5)^4)`, find `dy/dx`.
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Solve the following:
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10`x + 25x^2`
Solve the following.
If `y=root(5)((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `(dy) / (dx)` if, `y = e ^ (5x^2 - 2x + 4)`
If y = `root{5}{(3x^2 + 8x + 5)^4)`, find `(dy)/(dx)`
If `y = (x + sqrt(a^2 + x^2))^m`, prove that `(a^2 + x^2)(d^2y)/(dx^2) + xdy/dx - m^2y = 0`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/(dx)`.
