Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
xy = yx
Advertisements
उत्तर
xy = yx
Taking log on both sides
log xy = log yx
y log x = x log y
Differentiate with respect to x
`y xx 1/x + (log x) ("d"y)/("d"x) = x * 1/y xx ("d"y)/("d"x) + (log y) 1`
`y/x + (log x) ("d"y)/("d"x) = x/y * ("d"y)/("d"x) + log y`
`(log ) ("d"y)/("d"x) - x/y ("d"y)/("d"x) = log y - y/x`
`(log x - x/y) ("d"y)/("d"x) = log y - y/x`
`(y log x - x)/y * ("d"y)/("d"x) = (x log y - y)/x`
`("d"y)/("d"x) = y/x * (x log y - y)/(y log x - x)`
`("d"y)/("d"x) = (y (x log y - y))/(x(y log x - x))`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x + cos x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = ex sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = tan θ (sin θ + cos θ)
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = tan 3x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
Find the derivatives of the following:
If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`
Find the derivatives of the following:
If sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
