Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Advertisements
उत्तर
`sqrt(x) = "e"^((x - y))`
Squarting on both sides
`(sqrt(xy))^2 = ["e"^((x - y))]^2`
xy = `"e"^(2(x - y))` .......(1)
`x * ("d"y)/("d"x) + y * 1 = "e"^(2(x - y)) xx 2(1 - ("d"y)/("d"x))`
`x ("d"y)/("d"x) + y = 2"e"^(2(x - y)) - 2"e"^(2(x - y)) ("d"y)/("d"x)`
`x ("d"y)/("d"x) + 2"e"^(2(x - y)) ("d"y)/("d"x) = 2"e"^(2(x - y)) - y`
`[x + 2"e"^(2(x - y))] ("d"y)/("d"x) = 2"e"^(2(x - y)) - y`
`("d"y)/("d"x) = (2"e"^(2(x - y)) - y)/(x + 2"e"^(2(x - y))`
`("d"y)/("d"x) = (2xy - y)/(x + 2xy)`
By equation (1)
`("d"y)/("d"x) = (y(2x - 1))/(x(1 + 2y))`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = tan θ (sin θ + cos θ)
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x0
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = tan 3x
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
y = `x"e"^(-x^2)`
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
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) (2/pi sin x^circ)` is
Choose the correct alternative:
If y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` is
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a is
Choose the correct alternative:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)` then `("d"y)/("d"x)` is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
