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 x=at2, y= 2at , then find dy/dx.
If y =1 - cos θ , x = 1 - sin θ , then ` dy/dx at " "θ =pi/4` is ________
If x=a sin 2t(1+cos 2t) and y=b cos 2t(1−cos 2t), find `dy/dx `
If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t) then find `dy/dx `
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a cos θ, y = b cos θ
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(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 = sqrt(a^(sin^(-1)))`, y = `sqrt(a^(cos^(-1)))` show that `dy/dx = - y/x`
If `x = acos^3t`, `y = asin^3 t`,
Show that `(dy)/(dx) =- (y/x)^(1/3)`
The cost C of producing x articles is given as C = x3-16x2 + 47x. For what values of x, with the average cost is decreasing'?
If y = sin -1 `((8x)/(1 + 16x^2))`, find `(dy)/(dx)`
x = `"t" + 1/"t"`, y = `"t" - 1/"t"`
x = `(1 + log "t")/"t"^2`, y = `(3 + 2 log "t")/"t"`
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 `tan^-1 ((sqrt(1 + x^2) - 1)/x)` w.r.t. tan–1x, when x ≠ 0
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 = a sin" theta "and y = b cos" theta, "then" ("d"^2 "y")/"dx"^2` is equal to ____________.
If y `= "Ae"^(5"x") + "Be"^(-5"x") "x" "then" ("d"^2 "y")/"dx"^2` is equal to ____________.
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 ______.
