Advertisements
Advertisements
प्रश्न
sinx2 + sin2x + sin2(x2)
उत्तर
Let sinx2 + sin2x + sin2(x2)
∴ `"dy"/"dx" = "d"/"dx" sin(x^2) + "d"/"dx" (sinx)^2 + "d"/"dx" (sin x^2)^2`
= `cos(x^2) "d"/"dx" (x^2) + 2 sinx * "d"/"dx" (sin x) + 2 sinx^2 "d"/"dx" (sin x^2)`
= `2x cosx^2 + 2 sin x cos x + 2sinx^2 cosx^2 "d"/"dx" x^2`
= `2x cosx^2 + 2 sin x cos x + 2 sin x^2 cos x^2 xx 2x`
= 2x cos(x2) + sin 2x + 2x sin 2(x2)
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
`(sin (ax + b))/cos (cx + d)`
Differentiate w.r.t. x the function:
sin3 x + cos6 x
Differentiate w.r.t. x the function:
`(5x)^(3cos 2x)`
Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?
if y = `[(f(x), g(x), h(x)),(l, m,n),(a,b,c)]`, prove that `dy/dx` =`|(f'(x), g'(x), h'(x)),(l,m, n),(a,b,c)|`
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
If y = tan(x + y), find `("d"y)/("d"x)`
Let f(x)= |cosx|. Then, ______.
cos |x| is differentiable everywhere.
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)`
(sin x)cosx
sinmx . cosnx
(x + 1)2(x + 2)3(x + 3)4
`tan^-1 (secx + tanx), - pi/2 < x < pi/2`
`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 y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.
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 sin y = x sin (a + y), then value of dy/dx is
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 ______.
The set of all points where the function f(x) = x + |x| is differentiable, is ______.
