Advertisements
Advertisements
प्रश्न
IF `y = e^(sin-1x) and z =e^(-cos-1x),` prove that `dy/dz = e^x//2`
उत्तर
`y =e ^(sin-1x) and (z=e^(-cos-1x))`
`y/z = e^(sin-1x)/(e^(-cos-1x)) = e^(cos^-1 x+sin^-1x)`
`y/z = e^(pi/2)`
`y=e^(pi/2)z`
`dy/dz =e^(pi/2)dz/dz`
`dy/dz=e^(pi/2)(1)`
APPEARS IN
संबंधित प्रश्न
find dy/dx if x=e2t , y=`e^sqrtt`
If y =1 - cos θ , x = 1 - sin θ , then ` dy/dx at " "θ =pi/4` is ________
If x = a sin 2t (1 + cos2t) and y = b cos 2t (1 – cos 2t), find the values of `dy/dx `at t = `pi/4`
Find the value of `dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)`
If x = cos t (3 – 2 cos2 t) and y = sin t (3 – 2 sin2 t), find the value of dx/dy at t =4/π.
Derivatives of tan3θ with respect to sec3θ at θ=π/3 is
(A)` 3/2`
(B) `sqrt3/2`
(C) `1/2`
(D) `-sqrt3/2`
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx`
`x = 2at^2, y = at^4`
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = sin t, y = cos 2t
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a (θ – sin θ), y = a (1 + cos θ)
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
`x = (sin^3t)/sqrt(cos 2t), y = (cos^3t)/sqrt(cos 2t)`
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
`x = a(cos t + log tan t/2), y = a sin t`
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a sec θ, y = b tan θ
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)
If `x = sqrt(a^(sin^(-1)))`, y = `sqrt(a^(cos^(-1)))` show that `dy/dx = - y/x`
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`
x = `"e"^theta (theta + 1/theta)`, y= `"e"^-theta (theta - 1/theta)`
x = 3cosθ – 2cos3θ, y = 3sinθ – 2sin3θ
sin x = `(2"t")/(1 + "t"^2)`, tan y = `(2"t")/(1 - "t"^2)`
If x = ecos2t and y = esin2t, prove that `"dy"/"dx" = (-y log x)/(xlogy)`
If x = asin2t (1 + cos2t) and y = b cos2t (1–cos2t), show that `("dy"/"dx")_("at t" = pi/4) = "b"/"a"`
If x = 3sint – sin 3t, y = 3cost – cos 3t, find `"dy"/"dx"` at t = `pi/3`
Differentiate `x/sinx` w.r.t. sin x
If x = sint and y = sin pt, prove that `(1 - x^2) ("d"^2"y")/("dx"^2) - x "dy"/"dx" + "p"^2y` = 0
If x = t2, y = t3, then `("d"^2"y")/("dx"^2)` is ______.
If y `= "Ae"^(5"x") + "Be"^(-5"x") "x" "then" ("d"^2 "y")/"dx"^2` is equal to ____________.
If x = `a[cosθ + logtan θ/2]`, y = asinθ then `(dy)/(dx)` = ______.
Let a function y = f(x) is defined by x = eθsinθ and y = θesinθ, where θ is a real parameter, then value of `lim_(θ→0)`f'(x) is ______.
