Advertisements
Advertisements
Question
sinn (ax2 + bx + c)
Advertisements
Solution
Let y = sinn (ax2 + bx + c)
Differentiating both sides w.r.t. x
`"dy"/"dx" = "d"/"dx" sin^"n" ("a"x^2 + "b"x + "c")`
= `"n" * sin^("n" - 1) ("a"x^2 + "b"x + "c") * "d"/"dx" sin("a"x^2 + "b"x + "c")`
= `"n" * sin^("n" - 1) ("a"x^2 + "b"x + "c") * cos("a"x^2 + "b"x + "c") * "d"/"dx" ("a"x^2 + "b"x + "c")`
= `"n" * sin^("n" - 1) ("a"x^2 + "b"x + "c") * cos("a"x^2 + "b"x + "c") * (2"a"x + "b")`
Hence, `"dy"/"dx" = "n" (2"a"x + "b") * sin^("n" - 1)("a"x^2 + "b"x + "c")*cos("a"x^2 + "b"x + "c")`
APPEARS IN
RELATED QUESTIONS
Differentiate the function with respect to x.
sin (x2 + 5)
Differentiate the function with respect to x.
sin (ax + b)
Differentiate the function with respect to x.
`sec(tan (sqrtx))`
Differentiate the function with respect to x.
`cos (sqrtx)`
Differentiate the function with respect to x:
(3x2 – 9x + 5)9
Differentiate the function with respect to x:
sin3 x + cos6 x
Find `dy/dx`, if y = 12 (1 – cos t), x = 10 (t – sin t), `-pi/2 < t < pi/2`.
If f(x) = |x|3, show that f"(x) exists for all real x and find it.
Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?
Discuss the continuity and differentiability of the
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, ______.
If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.
| COLUMN-I | COLUMN-II |
| (A) If a function f(x) = `{((sin3x)/x, "if" x = 0),("k"/2",", "if" x = 0):}` is continuous at x = 0, then k is equal to |
(a) |x| |
| (B) Every continuous function is differentiable | (b) True |
| (C) An example of a function which is continuous everywhere but not differentiable at exactly one point |
(c) 6 |
| (D) The identity function i.e. f (x) = x ∀ ∈x R is a continuous function |
(d) False |
`cos(tan sqrt(x + 1))`
sinx2 + sin2x + sin2(x2)
(sin x)cosx
sinmx . cosnx
(x + 1)2(x + 2)3(x + 3)4
`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`
`tan^-1 (secx + tanx), - pi/2 < x < pi/2`
`tan^-1 (("a"cosx - "b"sinx)/("b"cosx - "a"sinx)), - pi/2 < x < pi/2` and `"a"/"b" tan x > -1`
If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0
The differential coefficient of `"tan"^-1 ((sqrt(1 + "x") - sqrt (1 - "x"))/(sqrt (1+ "x") + sqrt (1 - "x")))` is ____________.
A function is said to be continuous for x ∈ R, if ____________.
The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hours then in 25 hours, its number would be
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 ______.
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.
