Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x : `tan^-1((2^x)/(1 + 2^(2x + 1)))`
Advertisements
उत्तर
Let y = `tan^-1((2^x)/(1 + 2^(2x + 1)))`
= `tan^-1[(2.2^x - 2^x)/(1 + (2.2^x)(2^x))]`
= tan–1(2.2x) – tan–1(2x)
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[tan^-1(2.2^x) - tan^-1(2^x)]`
= `"d"/"dx"[tan^-1(2.2^x)] - "d"/"dx"[tan^-1(2^x)]`
= `(1)/(1 + (2.2^x)^2)."d"/"dx"(2.2^x) - (1)/(1 + (2^x)^2)."d"/"dx"(2^x)`
= `(1)/(1 + 4(2^(2x))) xx 2 xx 2^xlog2 - (1)/(1 + 2^(2x)) xx 2^xlog2`
= `2^xlog2[2/(1 + 4(2^(2x))) - 1/(1 + 2^(2x))]`.
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: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
Differentiate the following w.r.t.x: cos(x2 + a2)
Differentiate the following w.r.t.x: `log[tan(x/2)]`
Differentiate the following w.r.t.x:
tan[cos(sinx)]
Differentiate the following w.r.t.x: `log_(e^2) (log x)`
Differentiate the following w.r.t.x: (1 + 4x)5 (3 + x −x2)8
Differentiate the following w.r.t.x:
`(x^3 - 5)^5/(x^3 + 3)^3`
Differentiate the following w.r.t.x: (1 + sin2 x)2 (1 + cos2 x)3
Differentiate the following w.r.t.x:
`log(sqrt((1 - cos3x)/(1 + cos3x)))`
Differentiate the following w.r.t.x:
`log(sqrt((1 + cos((5x)/2))/(1 - cos((5x)/2))))`
Differentiate the following w.r.t.x: `log(sqrt((1 - sinx)/(1 + sinx)))`
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:
`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 : `cos^-1(sqrt((1 + cosx)/2))`
Differentiate the following w.r.t. x : `tan^-1[(1 + cos(x/3))/(sin(x/3))]`
Differentiate the following w.r.t. x : `"cosec"^-1[(10)/(6sin(2^x) - 8cos(2^x))]`
Differentiate the following w.r.t. x :
`sin^-1(4^(x + 1/2)/(1 + 2^(4x)))`
Differentiate the following w.r.t. x :
`sin^(−1) ((1 − x^3)/(1 + x^3))`
Differentiate the following w.r.t. x:
`tan^-1((2x^(5/2))/(1 - x^5))`
Differentiate the following w.r.t. x : `tan^-1((8x)/(1 - 15x^2))`
Differentiate the following w.r.t. x : `tan^-1((2sqrt(x))/(1 + 3x))`
Differentiate the following w.r.t. x : `tan^-1((a + btanx)/(b - atanx))`
Differentiate the following w.r.t. x :
`tan^-1((5 -x)/(6x^2 - 5x - 3))`
Differentiate the following w.r.t. x : `(x^5.tan^3 4x)/(sin^2 3x)`
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^(x^x) + e^(x^x)`
Differentiate the following w.r.t. x : (logx)x – (cos x)cotx
Differentiate the following w.r.t. x :
etanx + (logx)tanx
Differentiate the following w.r.t. x :
(sin x)tanx + (cos x)cotx
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)`
If f(x) is odd and differentiable, then f′(x) is
If y = `tan^-1[sqrt((1 + cos x)/(1 - cos x))]`, find `("d"y)/("d"x)`
y = {x(x - 3)}2 increases for all values of x lying in the interval.
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` = ______
If y = log (sec x + tan x), find `dy/dx`.
