Advertisements
Advertisements
प्रश्न
Differentiate the function with respect to x.
cos x3 . sin2 (x5)
Advertisements
उत्तर
Let, y = cos x3 . sin2 (x5)
`dy/dx = d/dx [cos x^3. sin^2 (x^5)]`
= `cos x^3 d/dx sin^2 (x^5) + sin^2 (x^5) d/dx cos x^3`
= `cos x^3 . 2 sin (x^5) d/dx sin (x^5) + sin^2 (x^5) (- sin x^3) d/dx (x^3)`
= `cos x^3 . 2 sin (x^5) cos (x^5) d/dx (x^5) + sin^2 (x^5) (- sin x^3) (3x^2)`
= `cos x^3 . 2 sin (x^5) cos (x^5) (5x^4) - sin^2 (x^5) sin x^3 . (3x^2)`
= `10x^4 cos x^3 sin(x^5) cos(x^5) - 3x^2 sin^2(x^5) sinx^3`
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.
`cos (sqrtx)`
Differentiate the function with respect to x:
`(5x)^(3cos 2x)`
Differentiate the function with respect to x:
`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`
Find `dy/dx`, if y = 12 (1 – cos t), x = 10 (t – sin t), `-pi/2 < t < pi/2`.
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?
Discuss the continuity and differentiability of the
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
If f(x) = x + 1, find `d/dx (fof) (x)`
If y = tan(x + y), find `("d"y)/("d"x)`
Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`
Let f(x)= |cosx|. Then, ______.
|sinx| is a differentiable function for every value of x.
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
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
`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 ______.
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 ____________.
If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` 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
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 ______.
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 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) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
The function f(x) = x | x |, x ∈ R is differentiable ______.
