If xy = yx, then xx - ylogxdydx is equal to :
yy - xlogy
yy + xlogy
xx + ylogx
xy - xlogy
fx = exsinx, then f6x = ?
e6xsin6x
- 8excosx
8exsinx
8excosx
If f(x) = 1 - 2sinxπ - 4x if x ≠ π4 a if x = π4is continuous at π4, then a is equal to :
4
2
1
14
If u = sin-1x2 + y2x + y then x∂u∂x + y∂u∂y is
sin(u)
tan(u)
cos(u)
cot(u)
If f(x, y) = cosx - 4ycosx + 4y, then ∂f∂xy = x2 is equal to
- 1
0
y = log1 + x1 - x14 - 12tan-1x, then dydx is equal to
x1 - x2
x21 - x4
x1 + x4
x1 - x4
x = cosθ, y = sin5θ ⇒ 1 - x2d2ydx2 - xdydx is equal to
- 5y
5y
25y
- 25y
D.
Given, x = cosθ, y = sin5θ dxdθ = - sinθ, dydθ = 5cos5θ∴ dydx = dydθdxdθ = - 5cos5θ sinθ⇒ d2ydx2 = ddxdydx = ddθdydx . dθdx = ddθ- 5cos5θ sinθ1- sinθ = sinθsin5θ . 25 + 5cos5θcosθsin2θ = - 25sin5θsin2θ - 5cos5θcosθsin3θNow, 1 - x2d2ydx2 - xdydx = 1 - cos2θ- 25sin5θsin2θ - 5cos5θcosθsin3θ - cosθ- 5cos5θ sinθ
= sin2θ- 25sin5θsin2θ - 5cos5θcosθsin3θ + 5cosθcos5θ sinθ = - 25sin(5θ) - 5cos5θcosθ sinθ + 5cos5θcosθ sinθ = - 25sin(5θ) = - 25y
If f : R → R is defined by fx = cos3x - cosxx2, for x ≠ 0 λ, for x = 0and if f is continuous at x = 0, then λ = ?
- 2
- 4
- 6
- 8
If f(2) = 4 and f'(2) = 1, thenlimx→2xf2 - 2fxx - 2 = ?
3
If y = sinlogex, then x2d2ydx2 + xdydx is equal to
y = sinlogex
coslogex
y2
- y