Advertisements
Advertisements
प्रश्न
If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.
विकल्प
`cos/(2y - 1)`
`cosx/(1 - 2y)`
`sinx/(1 - 2y)`
`sinx/(2y - 1)`
Advertisements
उत्तर
If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to `cos/(2y - 1)`.
Explanation:
Given that: y = `sqrt(sinx + y)`
Differentiating both sides w.r.t. x
`"dy"/"dx" = 1/(2sqrt(sinx + y)) * "d"/"dx" (sin x + y)`
⇒ `"dy"/"dx" = 1/(2sqrt(sinx + y)) * (cos x + "dy"/"dx")`
⇒ `"dy"/"dx" = 1/(2y) * [cos x + "dy"/"dx"]`
⇒ `"dy"/"dx" = cosx/(2y) + 1/(2y) * "dy"/"dx"`
⇒ `"dy"/"dx" - 1/(2y) * "dy"/"dx" = cosx/(2y)`
⇒ `(1 - 1/(2y))"dy"/"dx" = cosx/(2y)`
⇒ `((2y - 1)/(2y)) "dy"/"dx" = cosx/(2y)`
⇒ `"dy"/"dx" = cosx/(2y) xx (2y)/(2y - 1)`
⇒ `"dy"/"dx" = cosx/(2y - 1)`
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
sin (ax + b)
Differentiate the function with respect to x.
`(sin (ax + b))/cos (cx + d)`
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
Differentiate the function with respect to x.
`cos (sqrtx)`
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 sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
Let f(x) = x|x|, for all x ∈ R. Discuss the derivability of f(x) at x = 0
If y = tan(x + y), find `("d"y)/("d"x)`
cos |x| is differentiable everywhere.
Show that the function f(x) = |sin x + cos x| is continuous at x = π.
sinn (ax2 + bx + c)
sinx2 + sin2x + sin2(x2)
sinmx . cosnx
`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`
`tan^-1 (("a"cosx - "b"sinx)/("b"cosx - "a"sinx)), - pi/2 < x < pi/2` and `"a"/"b" tan x > -1`
`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 k be an integer, then `lim_("x" -> "k") ("x" - ["x"])` ____________.
If `"f"("x") = ("sin" ("e"^("x"-2) - 1))/("log" ("x" - 1)), "x" ne 2 and "f" ("x") = "k"` for x = 2, then value of k for which f is continuous is ____________.
A function is said to be continuous for x ∈ R, if ____________.
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 `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`
Let c, k ∈ R. If f(x) = (c + 1)x2 + (1 – c2)x + 2k and f(x + y) = f(x) + f(y) – xy, for all x, y ∈ R, then the value of |2(f(1) + f(2) + f(3) + ... + f(20))| is equal to ______.
Let f: R→R and f be a differentiable function such that f(x + 2y) = f(x) + 4f(y) + 2y(2x – 1) ∀ x, y ∈ R and f’(0) = 1, then f(3) + f’(3) is ______.
If f(x) = `{{:((sin(p + 1)x + sinx)/x,",", x < 0),(q,",", x = 0),((sqrt(x + x^2) - sqrt(x))/(x^(3//2)),",", x > 0):}`
is continuous at x = 0, then the ordered pair (p, q) is equal to ______.
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 function f(x) = x | x |, x ∈ R is differentiable ______.
