Advertisements
Advertisements
प्रश्न
sinn (ax2 + bx + c)
Advertisements
उत्तर
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
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.
`(sin (ax + b))/cos (cx + d)`
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:
`(5x)^(3cos 2x)`
Differentiate the function with respect to x:
`(cos^(-1) x/2)/sqrt(2x+7)`, −2 < x < 2
Differentiate the function with respect to x:
`x^(x^2 -3) + (x -3)^(x^2)`, for x > 3
If (x – a)2 + (y – b)2 = c2, for some c > 0, prove that `[1+ (dy/dx)^2]^(3/2)/((d^2y)/dx^2)` is a constant independent of a and b.
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?
If f(x) = x + 1, find `d/dx (fof) (x)`
If y = tan(x + y), find `("d"y)/("d"x)`
If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`
Let f(x)= |cosx|. Then, ______.
sinx2 + sin2x + sin2(x2)
(sin x)cosx
(x + 1)2(x + 2)3(x + 3)4
`tan^-1 (("a"cosx - "b"sinx)/("b"cosx - "a"sinx)), - pi/2 < x < pi/2` and `"a"/"b" tan x > -1`
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
`tan^-1 ((3"a"^2x - x^3)/("a"^3 - 3"a"x^2)), (-1)/sqrt(3) < x/"a" < 1/sqrt(3)`
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 ______.
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
`d/(dx)[sin^-1(xsqrt(1 - x) - sqrt(x)sqrt(1 - x^2))]` is equal to
If sin y = x sin (a + y), then value of dy/dx is
A particle is moving on a line, where its position S in meters is a function of time t in seconds given by S = t3 + at2 + bt + c where a, b, c are constant. It is known that at t = 1 seconds, the position of the particle is given by S = 7 m. Velocity is 7 m/s and acceleration is 12 m/s2. The values of a, b, c are ______.
Let S = {t ∈ R : f(x) = |x – π| (e|x| – 1)sin |x| is not differentiable at t}. Then the set S 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.
If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
Which expression defines the derivative of a real function \[f\] at a point \[c\] in its domain?
What is \[\frac{d}{dx}(\cos x)\]?
A function is differentiable at \[x=c\] when which condition holds?
Which limit is the left-hand derivative at \[x=c\]?
What is the practical condition for differentiability at a point?
When is a function differentiable on an open interval \[(a,b)\]?
For differentiability on a closed interval \[[a,b]\], which derivative is considered at \[b\]?
If \[f\] is differentiable at \[c\], which limit equals \[f'(c)\]?
