Advertisements
Advertisements
Question
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Solution
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
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x – 3 sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = t3 cos t
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 = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `x/(sin x + 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 = `5^((-1)/x)`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Find the derivatives of the following:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Choose the correct alternative:
If f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
If f(x) = `{{:(x - 5, "if" x ≤ 1),(4x^2 - 9, "if" 1 < x < 2),(3x + 4, "if" x ≥ 2):}` , then the right hand derivative of f(x) at x = 2 is
Choose the correct alternative:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
