Advertisements
Advertisements
Question
Differentiate the following:
y = `root(3)(1 + x^3)`
Advertisements
Solution
y = `root(3)(1 + x^3)`
y = `(1 + x^3)^(1/3)`
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
`("d"y)/("d"x) = 1/3 (1 + x^3)^(1/3 - 1) xx "d"/("d"x) (1 + x^3)`
`("d"y)/("d"x) = 1/3 (1 + x^3)^(- 2/3) (0 + 3x^2)`
`("d"y)/("d"x) = 1/3 1/(1 + x^3)^(2/3) xx 3x^2`
`("d"y)/("d"x) = x^2/(1 + x^3)^(2/3)`
= `x^2 (1 + x^3)^(- 2/3)`
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:
y = cosec x . cot x
Differentiate the following:
y = tan 3x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = sin2(cos kx)
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `"e"^(xcosx)`
Find the derivatives of the following:
xy = yx
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:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Find the derivatives of the following:
If u = `tan^-1 (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`
Find the derivatives of the following:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
Find the derivatives of the following:
If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y2 when x = 0
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` 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
