Advertisements
Advertisements
प्रश्न
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
उत्तर
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
= `(("t"^3 + 1)/("t"^3 - 1))^(1/4)`
s'(t) = `1/4(("t"^3 + 1)/("t"^3 - 1))^(1/4 - 1) xx "d"/("d"x) (("t"^3 + 1)/("t"^3 - 1))`
= `1/4 (("t"^3 + 1)/("t"^3 - 1))^(- 3/4) xx (("t"^3 - 1)(3"t"^2 + 0) - ("t"^2 + 0) - ("t"^3 + 1)(3"t"^2 - 0))/("t"^3 - 1)^2`
= `1/4 (("t"^3 + 1)/("t"^3 - 1))^(- 3/4) xx (3"t"^5 - 3"t"^2 - 3"t"^5 - 3"t"^2)/("t"^3 - 1)^2`
= `1/4 (("t"^3 + 1)/("t"^3 - 1))^(- 3/4) xx (- 6"t"^2)/("t"^3 - 1)^2`
= `(- 3"t"^2 xx ("t"^3 + 1)^(- 3/4))/(2("t"^3 - 1)^(- 3/4) ("t"^3 - 1)^2`
= `(- 3"t"^2 xx ("t"^3 + 1)^(- 3/4))/(2("t"^3 - 1)^(- 3/4 + 2)`
= `(- 3"t"^2)/(2("t"^3 + 1)^(3/4) ("t"^3 - 1)^((- 3 + 8)/4)`
s'(t) = `(- 3"t"^2)/(2("t"^3 + 1)^(3/4) ("t"^3 - 1)^(5/4))`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = x sin x cos x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Differentiate the following:
y = tan 3x
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
Find the derivatives of the following:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0
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"`
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:
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
