Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x : `tan^-1((8x)/(1 - 15x^2))`
Advertisements
उत्तर
Let y = `tan^-1((8x)/(1 - 15x^2))`
= `tan^-1[(5x + 3x)/(1 - (5x)(3x))]`
= tan–1(5x) + tan–1(3x)
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[tan^-1(5x) + tan^-1(3x)]`
= `"d"/"dx"[tan^-1(5x)] + "d"/"dx"[tan^-1(3x)]`
= `(1)/(1 + (5x)^2)."d"/"dx"(5x) + (1)/(1 + (3x)^2)."d"/"dx"(3x)`
= `(1)/(1 + 25x^2) xx 5 + (1)/(1 + 9x^2) xx 3`
= `(5)/(1 + 25x^2) + (3)/(1 + 9x^2)`
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t. x:
(x3 – 2x – 1)5
Differentiate the following w.r.t.x:
`(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`
Differentiate the following w.r.t.x: cot3[log(x3)]
Differentiate the following w.r.t.x: `5^(sin^3x + 3)`
Differentiate the following w.r.t.x: log[cos(x3 – 5)]
Differentiate the following w.r.t.x: sec[tan (x4 + 4)]
Differentiate the following w.r.t.x: `sinsqrt(sinsqrt(x)`
Differentiate the following w.r.t.x: `log[sec (e^(x^2))]`
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: `(1 + sinx°)/(1 - sinx°)`
Differentiate the following w.r.t.x:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Differentiate the following w.r.t.x:
`log[a^(cosx)/((x^2 - 3)^3 logx)]`
Differentiate the following w.r.t.x:
y = (25)log5(secx) − (16)log4(tanx)
Differentiate the following w.r.t. x :
cos3[cos–1(x3)]
Differentiate the following w.r.t. x : `sin^4[sin^-1(sqrt(x))]`
Differentiate the following w.r.t. x : `cot^-1[cot(e^(x^2))]`
Differentiate the following w.r.t. x : `cos^-1(sqrt((1 + cosx)/2))`
Differentiate the following w.r.t. x :
`cot^-1[(sqrt(1 + sin ((4x)/3)) + sqrt(1 - sin ((4x)/3)))/(sqrt(1 + sin ((4x)/3)) - sqrt(1 - sin ((4x)/3)))]`
Differentiate the following w.r.t. x : `sin^-1(2xsqrt(1 - x^2))`
Differentiate the following w.r.t. x:
`sin^-1 ((1 - 25x^2)/(1 + 25x^2))`
Differentiate the following w.r.t. x : `tan^-1((2sqrt(x))/(1 + 3x))`
Differentiate the following w.r.t. x : `cot^-1((4 - x - 2x^2)/(3x + 2))`
Differentiate the following w.r.t. x :
`(x + 1)^2/((x + 2)^3(x + 3)^4`
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:
`x^(x^x) + e^(x^x)`
Differentiate the following w.r.t. x : (logx)x – (cos x)cotx
Differentiate the following w.r.t. x : `[(tanx)^(tanx)]^(tanx) "at" x = pi/(4)`
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 : `sec((x^5 + y^5)/(x^5 - y^5))` = a2
If y = sin−1 (2x), find `("d"y)/(""d"x)`
Differentiate sin2 (sin−1(x2)) 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) = ________.
Derivative of (tanx)4 is ______
y = {x(x - 3)}2 increases for all values of x lying in the interval.
The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n = 2t2 + 3 and w = t2 - t + 2, then the rate of change of W with respect to t at t = 1 is ______
If f(x) = `(3x + 1)/(5x - 4)` and t = `(5 + 3x)/(x - 4)`, then f(t) is ______
The differential equation of the family of curves y = `"ae"^(2(x + "b"))` is ______.
If x2 + y2 - 2axy = 0, then `dy/dx` equals ______
If y = cosec x0, then `"dy"/"dx"` = ______.
The volume of a spherical balloon is increasing at the rate of 10 cubic centimetre per minute. The rate of change of the surface of the balloon at the instant when its radius is 4 centimetres, is ______
If x = p sin θ, y = q cos θ, then `dy/dx` = ______
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 ______.
Diffierentiate: `tan^-1((a + b cos x)/(b - a cos x))` w.r.t.x.
