Advertisements
Advertisements
Question
Find `"dy"/"dx"` ; if x = sin3θ , y = cos3θ
Advertisements
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 xpyq = (x + y)p+q then Prove that `dy/dx = y/x`
Find `bb(dy/dx)` in the following:
ax + by2 = cos y
Discuss extreme values of the function f(x) = x.logx
If ex + ey = e(x + y), then show that `dy/dx = -e^(y - x)`.
Find `"dy"/"dx"` if x = at2, y = 2at.
Find `"dy"/"dx"`, if : x = sinθ, y = tanθ
Differentiate `cos^-1((1 - x^2)/(1 + x^2)) w.r.t. tan^-1 x.`
Differentiate xx w.r.t. xsix.
Suppose that the functions f and g and their derivatives with respect to x have the following values at x = 0 and x = 1:
| x | f(x) | g(x) | f')x) | g'(x) |
| 0 | 1 | 5 | `(1)/(3)` | |
| 1 | 3 | – 4 | `-(1)/(3)` | `-(8)/(3)` |
(i) The derivative of f[g(x)] w.r.t. x at x = 0 is ......
(ii) The derivative of g[f(x)] w.r.t. x at x = 0 is ......
(iii) The value of `["d"/"dx"[x^(10) + f(x)]^(-2)]_(x = 1_` is ........
(iv) The derivative of f[(x + g(x))] w.r.t. x at x = 0 is ...
Differentiate the following w.r.t. x : `sin[2tan^-1(sqrt((1 - x)/(1 + x)))]`
Differentiate the following w.r.t. x : `tan^-1((sqrt(x)(3 - x))/(1 - 3x))`
If sin y = x sin (a + y), then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
If y = Aemx + Benx, show that y2 – (m + n)y1 + mny = 0.
If x = a t4 y = 2a t2 then `("d"y)/("d"x)` = ______
`(dy)/(dx)` of `2x + 3y = sin x` is:-
Differentiate w.r.t x (over no. 24 and 25) `e^x/sin x`
Find `(dy)/(dx)` if x + sin(x + y) = y – cos(x – y)
Find `(d^2y)/(dy^2)`, if y = e4x
Find `dy/dx if, x= e^(3t), y = e^sqrtt`
Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`
