Advertisements
Advertisements
Question
Differentiate the following w.r.t. x:
`(x^2 + 2)^4/(sqrt(x^2 + 5)`
Advertisements
Solution
Let y = `(x^2 + 2)^4/(sqrt(x^2 + 5)`
Differentiating w.r.t. x, we get
`dy/dx = d/dx [(x^2 + 2)^4/(sqrt (x^2 + 5))]`
`dy/dx = (sqrt (x^2 + 5) * d/dx (x^2 + 2)^4 - (x^2 + 2)^4 * d/dx (sqrt (x^2 + 5)))/(sqrt (x^2 + 5))^2`
`dy/dx = (sqrt (x^2 + 5) xx 4 (x^2 + 2)^3 * d/dx (x^2 + 2) - (x^2 + 2)^4 xx 1/(2 (sqrt (x^2 + 5))) * d/dx (x^2 + 5))/(x^2 + 5)`
`dy/dx = (sqrt (x^2 + 5) xx 4(x^2 + 2)^3 * (2x + 0) - (x^2 + 2)^4/(2 sqrt (x^2 + 5)) xx (2x + 0))/(x^2 + 5)`
`dy/dx = (8x (x^2 + 5) (x^2 + 2)^3 - x (x^2 + 2)^4)/(x^2 + 5)^(3/2)`
`dy/dx = (x (x^2 + 2)^3 [8 (x^2 + 5) - (x^2 + 2)])/(x^2 + 5)^(3/2)`
`dy/dx = (x (x^2 + 2)^3 (8x^2 + 40 - x^2 - 2))/(x^2 + 5)^(3/2)`
`dy/dx = (x (x^2 + 2)^3 (7x^2 + 38))/(x^2 + 5)^(3/2)`.
Notes
Question is modified as per the answer given in the textbook.
APPEARS IN
RELATED QUESTIONS
Differentiate the following w.r.t.x:
`(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`
Differentiate the following w.r.t.x: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
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:
`sqrt(e^((3x + 2) + 5)`
Differentiate the following w.r.t.x: `5^(sin^3x + 3)`
Differentiate the following w.r.t.x: `e^(log[(logx)^2 - logx^2]`
Differentiate the following w.r.t.x:
(x2 + 4x + 1)3 + (x3− 5x − 2)4
Differentiate the following w.r.t.x: `cot(logx/2) - log(cotx/2)`
Differentiate the following w.r.t.x: `(e^sqrt(x) + 1)/(e^sqrt(x) - 1)`
Differentiate the following w.r.t.x: log[tan3x.sin4x.(x2 + 7)7]
Differentiate the following w.r.t.x:
y = (25)log5(secx) − (16)log4(tanx)
Differentiate the following w.r.t. x : cot–1(4x)
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 : `cos^-1(sqrt((1 + cosx)/2))`
Differentiate the following w.r.t. x :
`cos^-1(sqrt(1 - cos(x^2))/2)`
Differentiate the following w.r.t. x : `"cosec"^-1((1)/(4cos^3 2x - 3cos2x))`
Differentiate the following w.r.t. x : `cot^-1((sin3x)/(1 + cos3x))`
Differentiate the following w.r.t.x:
tan–1 (cosec x + cot x)
Differentiate the following w.r.t. x : `cos^-1((sqrt(3)cosx - sinx)/(2))`
Differentiate the following w.r.t. x : cos–1(3x – 4x3)
Differentiate the following w.r.t. x :
`sin^(−1) ((1 − x^3)/(1 + x^3))`
Differentiate the following w.r.t. x : `tan^-1((8x)/(1 - 15x^2))`
Differentiate the following w.r.t. x : `tan^-1((2^x)/(1 + 2^(2x + 1)))`
Differentiate the following w.r.t. x : `cot^-1((a^2 - 6x^2)/(5ax))`
Differentiate the following w.r.t. x : `cot^-1((4 - x - 2x^2)/(3x + 2))`
Differentiate the following w.r.t. x: `x^(tan^(-1)x`
Differentiate the following w.r.t. x: xe + xx + ex + ee.
Differentiate the following w.r.t. x : (logx)x – (cos x)cotx
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `tan^-1((3x^2 - 4y^2)/(3x^2 + 4y^2))` = a2
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants: `log((x^20 - y^20)/(x^20 + y^20))` = 20
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `e^((x^7 - y^7)/(x^7 + y^7)` = a
Differentiate sin2 (sin−1(x2)) w.r. to x
Differentiate `sin^-1((2cosx + 3sinx)/sqrt(13))` w.r. to x
Differentiate `tan^-1((8x)/(1 - 15x^2))` w.r. to x
If y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ...... ∞)`, show that `("d"y)/("d"x) = (sin x)/(1 - 2y)`
If f(x) = 3x - 2 and g(x) = x2, then (fog)(x) = ________.
y = {x(x - 3)}2 increases for all values of x lying in the interval.
A particle moves so that x = 2 + 27t - t3. The direction of motion reverses after moving a distance of ______ units.
The value of `d/(dx)[tan^-1((a - x)/(1 + ax))]` is ______.
Let f(x) be a polynomial function of the second degree. If f(1) = f(–1) and a1, a2, a3 are in AP, then f’(a1), f’(a2), f’(a3) are in ______.
