Advertisements
Advertisements
प्रश्न
Find `"dy"/"dx"`, if : x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`
Advertisements
उत्तर
x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`
Differentiating x and y w.r.t. x, we get
`"dx"/"dm" = "d"/"dm"(sqrt(a^2 + m^2))`
= `(1)/(2sqrt(a^2 + m^2))."d"/"dm"(a^2 + m^2)`
= `(1)/(2sqrt(a^2 + m^2)) xx (0 + 2m) = m/sqrt(a^2 + m^2)`
and
`"dy"/"dm" = "d"/"dm"[log(a^2 + m^2)]`
= `(1)/(a^2 + m^2)."d"/"dm"(a^2 + m^2)`
= `(1)/(a^2 + m^2) xx (0 + 2m) = (2m)/(a^2 + m^2)`
∴ `"dy"/"dx" = (("dy"/"dm"))/(("dx"/"dm"))`
= `(((2m)/(a^2 + m^2)))/((m/sqrt(a^2 + m^2))`
= `(2)/sqrt(a^2 + m^2)`.
APPEARS IN
संबंधित प्रश्न
Find `bb(dy/dx)` in the following:
x2 + xy + y2 = 100
Examine the differentialibilty of the function f defined by
\[f\left( x \right) = \begin{cases}2x + 3 & \text { if }- 3 \leq x \leq - 2 \\ \begin{array}xx + 1 \\ x + 2\end{array} & \begin{array} i\text { if } - 2 \leq x < 0 \\\text { if } 0 \leq x \leq 1\end{array}\end{cases}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Differentiate tan-1 (cot 2x) w.r.t.x.
Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)
Find `"dy"/"dx"`, if : x = `(t + 1/t)^a, y = a^(t+1/t)`, where a > 0, a ≠ 1, t ≠ 0.
Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`
Find `"dy"/"dx"`, if : `x = cos^-1(4t^3 - 3t), y = tan^-1(sqrt(1 - t^2)/t)`.
Find `"dy"/"dx"` if : x = t2 + t + 1, y = `sin((pit)/2) + cos((pit)/2) "at" t = 1`
Find `"dy"/"dx"` if : x = t + 2sin (πt), y = 3t – cos (πt) at t = `(1)/(2)`
If x = `(t + 1)/(t - 1), y = (t - 1)/(t + 1), "then show that" y^2 + "dy"/"dx"` = 0.
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 = `e^(mtan^-1x)`, show that `(1 + x^2)(d^2y)/(dx^2) + (2x - m)"dy"/"dx"` = 0.
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 : eax+b
Find the nth derivative of the following : apx+q
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 y = sec (tan –1x), then `"dy"/"dx"` at x = 1, is equal to
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)?
Choose the correct option from the given alternatives :
If x = a(cosθ + θ sinθ), y = a(sinθ – θ cosθ), then `((d^2y)/dx^2)_(θ = pi/4)` = .........
Differentiate the following w.r.t. x : `tan^-1((sqrt(x)(3 - x))/(1 - 3x))`
Differentiate the following w.r.t. x : `cos^-1((sqrt(1 + x) - sqrt(1 - x))/2)`
Differentiate the following w.r.t. x:
`tan^-1(x/(1 + 6x^2)) + cot^-1((1 - 10x^2)/(7x))`
Differentiate the following w.r.t. x : `tan^-1[sqrt((sqrt(1 + x^2) + x)/(sqrt(1 + x^2) - x))]`
If y2 = a2cos2x + b2sin2x, show that `y + (d^2y)/(dx^2) = (a^2b^2)/y^3`
If log y = log (sin x) – x2, show that `(d^2y)/(dx^2) + 4x "dy"/"dx" + (4x^2 + 3)y` = 0.
If y = Aemx + Benx, show that y2 – (m + n)y1 + mny = 0.
Find `"dy"/"dx"` if, x3 + x2y + xy2 + y3 = 81
Choose the correct alternative.
If y = 5x . x5, then `"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 = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
State whether the following statement is True or False:
If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x) = 1/(2sqrt(x)) + 1/(2sqrt(y)) = 1/(2sqrt("a"))`
`(dy)/(dx)` of `xy + y^2 = tan x + y` is
Differentiate w.r.t x (over no. 24 and 25) `e^x/sin x`
If y = `e^(m tan^-1x)` then show that `(1 + x^2) (d^2y)/(dx^2) + (2x - m) (dy)/(dx)` = 0
If 2x + 2y = 2x+y, then `(dy)/(dx)` is equal to ______.
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/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)`
If log(x + y) = log(xy) + a then show that, `dy/dx=(-y^2)/x^2`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
If log(x + y) = log(xy) + a, then show that `dy/dx = (-y^2)/x^2`
