Advertisements
Advertisements
प्रश्न
Choose the correct alternative.
If ax2 + 2hxy + by2 = 0 then `"dy"/"dx" = ?`
विकल्प
`(("ax" + "hx"))/(("hx" + "by"))`
`(-("ax" + "hx"))/(("hx" + "by"))`
`(("ax" - "hx"))/(("hx" + "by"))`
`(("2ax" + "hy"))/(("hx" + "3by"))`
Advertisements
उत्तर
`(-("ax" + "hx"))/(("hx" + "by"))`
Explanation:
ax2 + 2hxy + by2 = 0
Differentiating both sides w.r.t.x, we get
`"a"(2"x") + "2h" * "d"/"dx" ("xy") + "b"("2y") "dy"/"dx" = 0`
∴ 2ax + 2h `["x" * "dy"/"dx" + "y"(1)] + 2"by" "dy"/"dx" = 0`
∴ 2ax + 2hx `"dy"/"dx"` + 2hy + 2by`"dy"/"dx"` = 0
∴ 2`"dy"/"dx"`(hx + by) = - 2ax - 2hy
∴ 2`"dy"/"dx" = (-2("ax" + "hy"))/(("hx" + "by"))`
∴ `"dy"/"dx" = (-("ax" + "hx"))/(("hx" + "by"))`
APPEARS IN
संबंधित प्रश्न
Find dy/dx if x sin y + y sin x = 0.
Find `bb(dy/dx)` in the following:
2x + 3y = sin x
Find `bb(dy/dx)` in the following:
2x + 3y = sin y
if `x^y + y^x = a^b`then Find `dy/dx`
If for the function
\[\Phi \left( x \right) = \lambda x^2 + 7x - 4, \Phi'\left( 5 \right) = 97, \text { find } \lambda .\]
Examine the differentialibilty of the function f defined by
\[f\left( x \right) = \begin{cases}2x + 3 & \text { if }- 3 \leq x \leq - 2 \\ \begin{array}xx + 1 \\ x + 2\end{array} & \begin{array} i\text { if } - 2 \leq x < 0 \\\text { if } 0 \leq x \leq 1\end{array}\end{cases}\]
Differentiate e4x + 5 w.r..t.e3x
Find `(dy)/(dx)` if `y = sin^-1(sqrt(1-x^2))`
If `sin^-1((x^5 - y^5)/(x^5 + y^5)) = pi/(6), "show that" "dy"/"dx" = x^4/(3y^4)`
Find `"dy"/"dx"`, if : x = sinθ, y = tanθ
Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`
Find `"dy"/"dx"` if : x = cosec2θ, y = cot3θ at θ= `pi/(6)`
If x = cos t, y = emt, show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" - m^2y` = 0.
Find the nth derivative of the following : cos (3 – 2x)
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 f(x) = `sin^-1((4^(x + 1/2))/(1 + 2^(4x)))`, which of the following is not the derivative of f(x)?
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 `tan^-1((sqrt(1 + x^2) - 1)/x)` w.r.t. `cos^-1(sqrt((1 + sqrt(1 + x^2))/(2sqrt(1 + x^2))))`
Find `"dy"/"dx"` if, yex + xey = 1
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"`
If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`
If x = a t4 y = 2a t2 then `("d"y)/("d"x)` = ______
If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
Find `(dy)/(dx)`, if `y = sin^-1 ((2x)/(1 + x^2))`
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`
