Advertisements
Advertisements
Question
Find `"dy"/"dx"` ; if x = sin3θ , y = cos3θ
Solution
x = sin3 θ
differentlating w.r.t. θ
`"dy"/("d" theta) = 3 "sin"^2 theta . "cos" theta`
Y = cos3θ
Differentiating w.r.t. θ
`"dy"/("d" theta) = 3"cos"^2 theta (-"sin" theta)`
= -3 cos2 θ . sin θ
`"dy"/"dx" = ("dy"/("d"theta))/("dx"/("d" theta)) = (-3"cos"^2 theta . "sin" theta)/(3"sin"^2 theta . "cos" theta) = ("- cos" theta)/("sin" theta) = - "cot" theta`
APPEARS IN
RELATED QUESTIONS
If y=eax ,show that `xdy/dx=ylogy`
Find `dy/dx` in the following:
2x + 3y = sin x
Find `dy/dx` in the following:
sin2 x + cos2 y = 1
Show that the derivative of the function f given by
Is |sin x| differentiable? What about cos |x|?
Write the derivative of f (x) = |x|3 at x = 0.
If \[\lim_{x \to c} \frac{f\left( x \right) - f\left( c \right)}{x - c}\] exists finitely, write the value of \[\lim_{x \to c} f\left( x \right)\]
If x = tan-1t and y = t3 , find `(dy)/(dx)`.
If y = `sqrt(cosx + sqrt(cosx + sqrt(cosx + ... ∞)`, then show that `"dy"/"dx" = sinx/(1 - 2y)`.
Find `"dy"/"dx"`, if : x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`
Find `"dy"/"dx"`, if : x = sinθ, y = tanθ
Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)
Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`
If x = at2 and y = 2at, then show that `xy(d^2y)/(dx^2) + a` = 0.
If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
If `sec^-1((7x^3 - 5y^3)/(7^3 + 5y^3)) = "m", "show" (d^2y)/(dx^2)` = 0.
If x2 + 6xy + y2 = 10, show that `(d^2y)/(dx^2) = (80)/(3x + y)^3`.
If x = a sin t – b cos t, y = a cos t + b sin t, show that `(d^2y)/(dx^2) = -(x^2 + y^2)/(y^3)`.
Find the nth derivative of the following : `(1)/(3x - 5)`
Choose the correct option from the given alternatives :
Let `f(1) = 3, f'(1) = -(1)/(3), g(1) = -4 and g'(1) =-(8)/(3).` The derivative of `sqrt([f(x)]^2 + [g(x)]^2` w.r.t. x at x = 1 is
Choose the correct option from the given alternatives :
If y = sin (2sin–1 x), then dx = ........
Choose the correct option from the given alternatives :
If `xsqrt(y + 1) + ysqrt(x + 1) = 0 and x ≠ y, "then" "dy"/"dx"` = ........
If x sin (a + y) + sin a . cos (a + y) = 0, then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
If `x = e^(x/y)`, then show that `"dy"/"dx" = (x - y)/(xlogx)`
Differentiate log `[(sqrt(1 + x^2) + x)/(sqrt(1 + x^2 - x)]]` w.r.t. cos (log x).
Solve the following:
If `"x"^5 * "y"^7 = ("x + y")^12` then show that, `"dy"/"dx" = "y"/"x"`
Choose the correct alternative.
If y = 5x . x5, then `"dy"/"dx" = ?`
If `"x"^7*"y"^9 = ("x + y")^16`, then show that `"dy"/"dx" = "y"/"x"`
Find `"dy"/"dx"` if x = `"e"^"3t", "y" = "e"^(sqrt"t")`.
`(dy)/(dx)` of `xy + y^2 = tan x + y` is
Find `(d^2y)/(dy^2)`, if y = e4x
If 2x + 2y = 2x+y, then `(dy)/(dx)` is equal to ______.
Find `dy/dx` if , x = `e^(3t), y = e^(sqrtt)`
Find `dy / dx` if, x = `e^(3t), y = e^sqrt t`
Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`
Find `dy/dx"if", x= e^(3t), y=e^sqrtt`
If log(x + y) = log(xy) + a, then show that `dy/dx = (-y^2)/x^2`
