Advertisements
Advertisements
प्रश्न
Derivatives of tan3θ with respect to sec3θ at θ=π/3 is
(A)` 3/2`
(B) `sqrt3/2`
(C) `1/2`
(D) `-sqrt3/2`
Advertisements
उत्तर
(B) `sqrt3/2`
Let `y = tan^3theta , and x = sec^3theta`
`dy/(d theta)=3tan^2theta.sec^2theta, dx/(d theta)=3sec^2theta.secthetatantheta`
`dy/dx=sintheta=sin(pi/3)=sqrt3/2`
APPEARS IN
संबंधित प्रश्न
If `log_10((x^3-y^3)/(x^3+y^3))=2 "then show that" dy/dx = [-99x^2]/[101y^2]`
If x = f(t), y = g(t) are differentiable functions of parammeter ‘ t ’ then prove that y is a differentiable function of 'x' and hence, find dy/dx if x=a cost, y=a sint
If x=at2, y= 2at , then find dy/dx.
If `x=a(t-1/t),y=a(t+1/t)`, then show that `dy/dx=x/y`
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) then find `dy/dx `
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.
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = a cos θ, y = b cos θ
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = sin t, y = cos 2t
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = a (θ – sin θ), y = a (1 + cos θ)
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = `a(cos t + log tan t/2)`, y = a sin t
If `x = acos^3t`, `y = asin^3 t`,
Show that `(dy)/(dx) =- (y/x)^(1/3)`
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`
If X = f(t) and Y = g(t) Are Differentiable Functions of t , then prove that y is a differentiable function of x and
`"dy"/"dx" =("dy"/"dt")/("dx"/"dt" ) , "where" "dx"/"dt" ≠ 0`
Hence find `"dy"/"dx"` if x = a cos2 t and y = a sin2 t.
IF `y = e^(sin-1x) and z =e^(-cos-1x),` prove that `dy/dz = e^x//2`
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 = `"e"^theta (theta + 1/theta)`, y= `"e"^-theta (theta - 1/theta)`
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
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 = t2, y = t3, then `("d"^2"y")/("dx"^2)` is ______.
Derivative of x2 w.r.t. x3 is ______.
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 ____________.
Form the point of intersection (P) of lines given by x2 – y2 – 2x + 2y = 0, points A, B, C, Dare taken on the lines at a distance of `2sqrt(2)` units to form a quadrilateral whose area is A1 and the area of the quadrilateral formed by joining the circumcentres of ΔPAB, ΔPBC, ΔPCD, ΔPDA is A2, then `A_1/A_2` equals
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 ______.
