Advertisements
Advertisements
Question
Find `"dy"/"dx" if, sqrt"x" + sqrt"y" = sqrt"a"`
Advertisements
Solution
`sqrt"x" + sqrt"y" = sqrt"a"`
Differentiating both sides w.r.t. x, we get
`1/(2 sqrt"x") + 1/(2sqrt"y") * "dy"/"dx" = 0`
∴ `1/(2sqrt"y") * "dy"/"dx" = (-1)/(2sqrt"x")`
∴ `"dy"/"dx" = - sqrt("y"/"x")`
APPEARS IN
RELATED QUESTIONS
Find dy/dx if x sin y + y sin x = 0.
Show that the derivative of the function f given by
Examine the differentialibilty of the function f defined by
\[f\left( x \right) = \begin{cases}2x + 3 & \text { if }- 3 \leq x \leq - 2 \\ \begin{array}xx + 1 \\ x + 2\end{array} & \begin{array} i\text { if } - 2 \leq x < 0 \\\text { if } 0 \leq x \leq 1\end{array}\end{cases}\]
Is |sin x| differentiable? What about cos |x|?
If f (x) = |x − 2| write whether f' (2) exists or not.
Find `"dy"/"dx"` ; if x = sin3θ , y = cos3θ
Find `(dy)/(dx) , "If" x^3 + y^2 + xy = 10`
Find `(dy)/(dx)` if `y = sin^-1(sqrt(1-x^2))`
Find `"dy"/"dx"` if x = at2, y = 2at.
Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)
DIfferentiate x sin x w.r.t. tan x.
Find `(d^2y)/(dx^2)` of the following : x = a cos θ, y = b sin θ at θ = `π/4`.
If y = sin (m cos–1x), then show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" + m^2y` = 0.
Find the nth derivative of the following : cos x
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
Solve the following :
f(x) = –x, for – 2 ≤ x < 0
= 2x, for 0 ≤ x < 2
= `(18 - x)/(4)`, for 2 < x ≤ 7
g(x) = 6 – 3x, for 0 ≤ x < 2
= `(2x - 4)/(3)`, for 2 < x ≤ 7
Let u (x) = f[g(x)], v(x) = g[f(x)] and w(x) = g[g(x)]. Find each derivative at x = 1, if it exists i.e. find u'(1), v' (1) and w'(1). If it doesn't exist, then explain why?
Differentiate the following w.r.t. x:
`tan^-1(x/(1 + 6x^2)) + cot^-1((1 - 10x^2)/(7x))`
If log y = log (sin x) – x2, show that `(d^2y)/(dx^2) + 4x "dy"/"dx" + (4x^2 + 3)y` = 0.
Find `"dy"/"dx"` if, x3 + x2y + xy2 + y3 = 81
If `"x"^5 * "y"^7 = ("x + y")^12` then show that, `"dy"/"dx" = "y"/"x"`
If y = `("x" + sqrt("x"^2 - 1))^"m"`, then `("x"^2 - 1) "dy"/"dx"` = ______.
State whether the following is True or False:
The derivative of `"x"^"m"*"y"^"n" = ("x + y")^("m + n")` is `"x"/"y"`
y = `e^(x3)`
If 2x + 2y = 2x+y, then `(dy)/(dx)` is equal to ______.
Let y = y(x) be a function of x satisfying `ysqrt(1 - x^2) = k - xsqrt(1 - y^2)` where k is a constant and `y(1/2) = -1/4`. Then `(dy)/(dx)` at x = `1/2`, is equal to ______.
If y = `sqrt(tan x + sqrt(tanx + sqrt(tanx + .... + ∞)`, then show that `dy/dx = (sec^2x)/(2y - 1)`.
Find `dy/dx` at x = 0.
If log (x+y) = log (xy) + a then show that, `dy/dx= (-y^2)/(x^2)`
