Advertisements
Advertisements
Question
Differentiate the following w.r.t.x:
`(x^3 - 5)^5/(x^3 + 3)^3`
Advertisements
Solution
Let y = `(x^3 - 5)^5/(x^3 + 3)^3`
Differentiating w.r.t.x, we get
`"dy"/"dx" = "d"/"dx"[(x^3 - 5)^5/(x^3 + 3)^3]`
`"dy"/"dx" = [(x^3 + 3)^3 × "d"/"dx"(x^3 - 5)^5 - (x^3 - 5)^5 "d"/"dx" (x^3 + 3)^3]/[(x^3 + 3)^3]^2`
`"dy"/"dx" = [(x^3 + 3)^3 × 5(x^3 - 5)^4 × "d"/"dx"(x^3 - 5) - (x^3 - 5)^5 × 3(x^3 + 3)^2 × "d"/"dx" (x^3 + 3)]/(x^3 + 3)^6`
`"dy"/"dx" = [(x^3 + 3)^3 × 5(x^3 - 5)^4 × (3x^2 - 0) - (x^3 - 5)^5 × 3(x^3 + 3)^2 × (3x^2 + 0)]/(x^3 + 3)^6`
`"dy"/"dx" = [3x^2(x^3 + 3)^2(x^3 - 5)^4[5(x^3 + 3) - 3(x^3 - 5)]]/(x^3 + 3)^6`
`"dy"/"dx" = [3x^2(x^3 + 3)^2(x^3 - 5)^4[5x^3 + 15 - 3x^3 + 15]]/(x^3 + 3)^6`
`"dy"/"dx" = [3x^2cancel((x^3 + 3)^2)(x^3 - 5)^4(2x^3 + 30)]/(x^3 + 3)^(cancel(6)4)`
`"dy"/"dx" = [3x^2(x^3 - 5)^4(2x^3 + 30)]/(x^3 + 3)^4`
`"dy"/"dx" = [3x^2(x^3 - 5)^4 . 2(x^3 + 15)]/(x^3 + 3)^4`
`"dy"/"dx" = [6x^2(x^3 + 15)(x^3 - 5)^4]/(x^3 + 3)^4`
APPEARS IN
RELATED QUESTIONS
Differentiate the following w.r.t. x:
(x3 – 2x – 1)5
Differentiate the following w.r.t.x:
`(sqrt(3x - 5) - 1/sqrt(3x - 5))^5`
Differentiate the following w.r.t.x: cos(x2 + a2)
Differentiate the following w.r.t.x: log[cos(x3 – 5)]
Differentiate the following w.r.t.x:
tan[cos(sinx)]
Differentiate the following w.r.t.x: `e^(log[(logx)^2 - logx^2]`
Differentiate the following w.r.t.x: `sinsqrt(sinsqrt(x)`
Differentiate the following w.r.t.x: [log {log(logx)}]2
Differentiate the following w.r.t.x:
sin2x2 – cos2x2
Differentiate the following w.r.t.x:
(x2 + 4x + 1)3 + (x3− 5x − 2)4
Differentiate the following w.r.t.x:
log (sec 3x+ tan 3x)
Differentiate the following w.r.t. x : cot–1(x3)
Differentiate the following w.r.t. x : `tan^-1(sqrt(x))`
Differentiate the following w.r.t. x:
`sin^-1(sqrt((1 + x^2)/2))`
Differentiate the following w.r.t. x : `sin^-1(x^(3/2))`
Differentiate the following w.r.t. x :
cos3[cos–1(x3)]
Differentiate the following w.r.t. x : `"cosec"^-1[1/cos(5^x)]`
Differentiate the following w.r.t. x : `cos^-1(sqrt((1 + cosx)/2))`
Differentiate the following w.r.t. x : `"cosec"^-1((1)/(4cos^3 2x - 3cos2x))`
Differentiate the following w.r.t. x : `tan^-1(sqrt((1 + cosx)/(1 - cosx)))`
Differentiate the following w.r.t. x : `sin^-1((cossqrt(x) + sinsqrt(x))/sqrt(2))`
Differentiate the following w.r.t. x :
`cos^-1[(3cos(e^x) + 2sin(e^x))/sqrt(13)]`
Differentiate the following w.r.t. x : `"cosec"^-1[(10)/(6sin(2^x) - 8cos(2^x))]`
Differentiate the following w.r.t. x :
`cos^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x : `sin^-1(2xsqrt(1 - x^2))`
Differentiate the following w.r.t. x :
`cos^-1 ((1 - 9^x))/((1 + 9^x)`
Differentiate the following w.r.t. x:
`tan^-1((2x^(5/2))/(1 - x^5))`
Differentiate the following w.r.t. x : `root(3)((4x - 1)/((2x + 3)(5 - 2x)^2)`
Differentiate the following w.r.t. x : `(x^2 + 3)^(3/2).sin^3 2x.2^(x^2)`
Differentiate the following w.r.t. x : (sin x)x
Differentiate the following w.r.t. x: (sin xx)
Differentiate the following w.r.t. x: xe + xx + ex + ee.
Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`
Differentiate the following w.r.t. x : `10^(x^(x)) + x^(x(10)) + x^(10x)`
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : x7.y5 = (x + y)12
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `cos^-1((7x^4 + 5y^4)/(7x^4 - 5y^4)) = tan^-1a`
If f(x) is odd and differentiable, then f′(x) is
Differentiate sin2 (sin−1(x2)) w.r. to x
Differentiate `sin^-1((2cosx + 3sinx)/sqrt(13))` w.r. to x
If y = `sin^-1[("a"cosx - "b"sinx)/sqrt("a"^2 + "b"^2)]`, then find `("d"y)/("d"x)`
If the function f(x) = `(log (1 + "ax") - log (1 - "bx))/x, x ≠ 0` is continuous at x = 0 then, f(0) = _____.
If x2 + y2 - 2axy = 0, then `dy/dx` equals ______
Let f(x) = `(1 - tan x)/(4x - pi), x ne pi/4, x ∈ [0, pi/2]`. If f(x) is continuous in `[0, pi/2]`, then f`(pi/4)` is ______.
If x = eθ, (sin θ – cos θ), y = eθ (sin θ + cos θ) then `dy/dx` at θ = `π/4` is ______.
