Advertisements
Advertisements
प्रश्न
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
Advertisements
उत्तर
sin y = x sin(a + y)
⇒ `x = sin y/(sin (a + y))` ....(i)
Differentiating (i) w.r.t.x,
⇒ 1 = `(sin(a + y).(d/dx sin y) - sin y. (d/dx sin (a + y)))/sin^2 (a + y)`
⇒ ` sin(a + y).cos y - d/dx - sin y. cos (a + y). d/dx = sin^2 (a + y)`]
⇒ `d/dx [ sin ( a + y) . cos y - sin y. cos ( a + y)] = sin^2 (a + y)`
⇒ `dy/dx[ sin ( a + y - y)] = sin^2 (a + y)`
⇒ `dy/dx = (sin^2 (a + y))/(sin a)`
Hence proved.
संबंधित प्रश्न
Differentiate the function with respect to x.
sin (x2 + 5)
Differentiate the function with respect to x.
cos (sin x)
Differentiate the function with respect to x.
cos x3 . sin2 (x5)
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
Prove that the function f given by f(x) = |x − 1|, x ∈ R is not differentiable at x = 1.
Differentiate the function with respect to x:
`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`
Discuss the continuity and differentiability of the
If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`
Differential coefficient of sec (tan–1x) w.r.t. x is ______.
|sinx| is a differentiable function for every value of x.
Show that the function f(x) = |sin x + cos x| is continuous at x = π.
`cos(tan sqrt(x + 1))`
`sin^-1 1/sqrt(x + 1)`
(x + 1)2(x + 2)3(x + 3)4
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`
If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0
If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.
For the curve `sqrt(x) + sqrt(y)` = 1, `"dy"/"dx"` at `(1/4, 1/4)` is ______.
If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` is
If sin y = x sin (a + y), then value of dy/dx is
If f(x) = `{{:(ax + b; 0 < x ≤ 1),(2x^2 - x; 1 < x < 2):}` is a differentiable function in (0, 2), then find the values of a and b.
The set of all points where the function f(x) = x + |x| is differentiable, is ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
