Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t.x:
sin2x2 – cos2x2
Advertisements
उत्तर
Let y = sin2x2 – cos2x2
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[sin^2x^2 - cos^2x^2]`
= `"d"/"dx"(sinx^2)^2 - "d"/"dx"(cosx^2)^2`
= `2sinx^2."d"/"dx"(sinx^2) - 2cosx^2."d"/"dx"(cosx^2)`
= `2sinx^2.cosx^2."d"/"dx"(x^2) - 2cosx^2.(-sinx^2)."d"/"dx"(x^2)`
= 2sin x2 . cos x2 x 2x + 2sinx2 . cosx2 x 2x
= 4x (2sinx2 . cosx2)
= 4x sin(2x2).
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t.x: `"cosec"(sqrt(cos x))`
Differentiate the following w.r.t.x: log[cos(x3 – 5)]
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:
(x2 + 4x + 1)3 + (x3− 5x − 2)4
Differentiate the following w.r.t.x: (1 + sin2 x)2 (1 + cos2 x)3
Differentiate the following w.r.t.x: `(e^sqrt(x) + 1)/(e^sqrt(x) - 1)`
Differentiate the following w.r.t.x: `log[4^(2x)((x^2 + 5)/(sqrt(2x^3 - 4)))^(3/2)]`
Differentiate the following w.r.t.x: `log[(ex^2(5 - 4x)^(3/2))/root(3)(7 - 6x)]`
Differentiate the following w. r. t. x.
cos–1(1 – x2)
Differentiate the following w.r.t. x : `sin^-1(x^(3/2))`
Differentiate the following w.r.t. x : `"cosec"^-1[1/cos(5^x)]`
Differentiate the following w.r.t. x :
`cos^-1(sqrt(1 - cos(x^2))/2)`
Differentiate the following w.r.t. x : `cot^-1((sin3x)/(1 + cos3x))`
Differentiate the following w.r.t. x : `tan^-1(sqrt((1 + cosx)/(1 - cosx)))`
Differentiate the following w.r.t. x : `cos^-1((sqrt(3)cosx - sinx)/(2))`
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:
`cot^-1((1 + 35x^2)/(2x))`
Differentiate the following w.r.t. x :
`tan^(−1)[(2^(x + 2))/(1 − 3(4^x))]`
Differentiate the following w.r.t. x : `((x^2 + 2x + 2)^(3/2))/((sqrt(x) + 3)^3(cosx)^x`
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 : (logx)x – (cos x)cotx
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 : x7.y5 = (x + y)12
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
If y is a function of x and log (x + y) = 2xy, then the value of y'(0) = ______.
Differentiate y = etanx w.r. to x
If f(x) is odd and differentiable, then f′(x) is
Differentiate `tan^-1((8x)/(1 - 15x^2))` 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) = _____.
Derivative of (tanx)4 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"` = ______.
If x = p sin θ, y = q cos θ, then `dy/dx` = ______
Differentiate `tan^-1 (sqrt((3 - x)/(3 + x)))` w.r.t. x.
