Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = 4 sec t + tan 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 = sin x0
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:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
y = `x^(logx) + (logx)^x`
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:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
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 = cos (sin x2), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is
Choose the correct alternative:
If x = a sin θ and y = b cos θ, then `("d"^2y)/("d"x^2)` is
Choose the correct alternative:
If f(x) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
