Advertisements
Advertisements
Question
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Advertisements
Solution
y = `(x^2 + 1) root(3)(x^2 + 2)`
y = `(x^2 + 1) (x^2 + 2)^(1/3)`
`("d"y)/("d"x) = (x^2 + 1)^(1/3) (x^2 + 2)^(1/3- 1) (2x + 0) + (x^2 + 2)^(1/3) (2x + 0)`
`("d"y)/("d"x) = 1/3 (x^2 + 1) (x^2 + 2)^(- 2/3) xx 2x + (x^2 + 2)^(1/3) (2x)`
= `(2x(x^2 + 1))/(3(x^2 + 2)^(2/3)) + 2x (x^2 + 2)^(1/3)`
= `(2x(x^2 + 1) + 2x(x^2 + 2)^(1/3) * 3(x^2 + 2)^(2/3))/(3(x^2 + 2)^(2/3)`
= `(2x^3 + 2x + 6x (x^2 + 2)^(1/3 + 2/3))/(3(x^2 + 2)^(2/3)`
= `(2x^2 + 2x + 6x(x^2 + 2))/(3(x^2 + 2)^(2/3)`
= `(2x^3 + 2x + 6x^3 + 12x)/(3(x^2 + 2)^(2/3)`
`("d"y)/("d"x) = (8x^3 + 14x)/(3(x^2 + 2)^(2/3)`
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cos x – 2 tan 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 = `(tanx - 1)/secx`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot 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:
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Differentiate the following:
y = tan 3x
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = sin3x + cos3x
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
x = a (cos t + t sin t); y = a (sin t – t cos t)
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
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
