Advertisements
Advertisements
प्रश्न
State whether the following is True or False:
The derivative of `"x"^"m"*"y"^"n" = ("x + y")^("m + n")` is `"x"/"y"`
पर्याय
True
False
उत्तर
False
APPEARS IN
संबंधित प्रश्न
Find dy/dx if x sin y + y sin x = 0.
Find `dy/dx` in the following:
2x + 3y = sin y
Find `dx/dy` in the following.
x2 + xy + y2 = 100
Find `dy/dx` in the following:
sin2 x + cos2 y = 1
Find `dy/dx` in the following:
`y = sin^(-1)((2x)/(1+x^2))`
if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`
Show that the derivative of the function f given by
If for the function
\[\Phi \left( x \right) = \lambda x^2 + 7x - 4, \Phi'\left( 5 \right) = 97, \text { find } \lambda .\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
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 = a cot θ, y = b cosec θ
Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)
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)`
Differentiate `tan^-1((x)/(sqrt(1 - x^2))) w.r.t. sec^-1((1)/(2x^2 - 1))`.
Differentiate `tan^-1((cosx)/(1 + sinx)) w.r.t. sec^-1 x.`
Find `(d^2y)/(dx^2)` of the following : x = sinθ, y = sin3θ at θ = `pi/(2)`
If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
If y = eax.sin(bx), show that y2 – 2ay1 + (a2 + b2)y = 0.
If y = sin (m cos–1x), then show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" + m^2y` = 0.
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)` = .........
Differentiate the following w.r.t. x:
`tan^-1(x/(1 + 6x^2)) + cot^-1((1 - 10x^2)/(7x))`
If y2 = a2cos2x + b2sin2x, show that `y + (d^2y)/(dx^2) = (a^2b^2)/y^3`
Find `"dy"/"dx" if, sqrt"x" + sqrt"y" = sqrt"a"`
Find `"dy"/"dx"` if, yex + xey = 1
Choose the correct alternative.
If y = 5x . x5, then `"dy"/"dx" = ?`
Choose the correct alternative.
If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2` then `"dy"/"dx"` = ?
If `"x"^"a"*"y"^"b" = ("x + y")^("a + b")`, then show that `"dy"/"dx" = "y"/"x"`
`(dy)/(dx)` of `2x + 3y = sin x` is:-
Differentiate w.r.t x (over no. 24 and 25) `e^x/sin x`
If 2x + 2y = 2x+y, then `(dy)/(dx)` is equal to ______.
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^sqrt t`
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`