c If f" (x) = 18 cos 3x and f' (0) = f(5) = 1, find f(x).

Q: Find the particular solution for: y' sin(2y) - cosx = 0, x =when y = 0 %3D 2

A:

Q: use appropriate substitution to solve differential equatio dy/dx-(2/x)y=-x^2y^3

A:

Q: 12. cos cos (xy) = 1+ sin y

A:

Q: dx (2) 3y sin x 2xy cos x = 0 dy (3) 3x²y² + 2x³y -= 0

A:

Q: d [ sin(x)cos(x) dx dx 1+x4

A: Find the integral

Q: Find the differential dy of the given function y=extanx

A:

Q: 1. Find the first derivative of the given function given. a. y = sint cos t b. y = 6 tan(2n + 3x)

A: In this question we have to find the first derivate of the given function.

Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

A:

Q: Let z= sin (y2 – 4x), Find the rate of change of z with respect to y at the point (2, 1) with x held…

A:

Q: dy by implicit differentiation if dx 3 9. = 1. Find - -

A: The given function is 3y+9x=1

Q: 13. We know that x = r cos 0 and y = r sin 0, then find the derivative af/ar if 1 f = ? + y?

A:

Q: - sinx) dx 2. 1. (COSX (ax' +b)*x dx 2. 2/3

A:

Q: Let y=(x2+3) to the 2nd power. Find the differential dy when x=4 and dx=0.2 ?????????? Find the…

A:

Q: Sx-3) (sin (In x) + cos (In x)} dx equals

A: Here we have to evaluate I=∫(x-3)sin-1lnx+cos-1lnxdx

Q: Ssint2x)dx = 2cos(2x) (2x) + С -cos(2x) + C O 2 cos(2x) -cos(2x)+ C

A:

Q: 2- X %3D +2 3- Coshx dy +(y sinh x+e) dxo 36

A:

Q: 3e"dx 3x 1. 3x – 16 2. x 10 – 3x°dx 3. / In (cos®) an@ de 3.

A:

Q: for (e3x+y2)5 = sin x cos y, find dy/dx. using implicit differentiation. must show all steps

A:

Q: Let z=sin (y 2- 4x). Find the rate of change of z with respect to y at the point (2, 1) with x held…

A:

Q: 1. S e sin 4x cos 4x dx 2. S dx Je-2x dx e 2x

A:

Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y2 + z²; x = p sin o…

A: Given:  w = 12x2+12y2+z2 x=ρ sinϕ cosθ, y=ρ sinϕ sin θ, z= ρ cosϕ  Find: ∂w∂ρ, ∂w∂ϕ and ∂w∂θ Chain…

Q: Ssin (2x)cos(2r)dx

A:

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

A:

Q: Find the differential of the function y=xxe2x at the point x=1.

A:

Q: Find the second derivative 1. y = In(x^3+1) 2. y = Arctan (e^x)

A: Given: y=lnx3+1, y=tan-1ex

Q: Find the differential of the function y=2x2+3x+1 at the point x=1 when dx=0,1.

A: To find the differential of the given function at point x = 1 when (d x) = 0, 1.

Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given acceleration, a(t)=cost,       t>0 And v(0)=0, x(0)=3

Q: 4- cosh x2 dy + (sinh x)y = e-* dx

A:

Q: dy/dx of y=cos^-1 (e^-3x)

A: Given y=cos-1e-3x

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: y = (cos x-x4+ 1/x2)5 - In (3x+1)  Find dy/dx

A: =?

Q: Ssin^3 (2/3 x) cos^4 (2/3 x) dx

A:

Q: ( cos nx dx= [cos %3D nx cos nx dx 0. %D

A: We have to find the integral of cos2nx dx from 0 to 2pi.

Q: tan(4x + 8). Find the differential dy when x = Let y 1 and dæx 0.3 Find the differential dy when x =…

A: In the given question we have to find dy of the function at both of the given value.

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

A:

Q: (a) By using the chain rule and the derivative if x>0 (1, -1, if x< O' d (\xl) = dx | d find - (lx3…

A: Just break the mod function in two parts and easily calculate the derivative.

Q: – cos(4x) dx V 1+ cos(4x) d 1-

A:

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: Find the differential of the function. y=x^4 (sin(8x))

A: topic:-  derivatives

Q: Find the derivative. d | dx + 0 OA. x³ sin (x¹) +5, ○ B. sint dt C. 4x³ sin (x4) - cos (x4) - 1 D.…

A:

Q: Find dx (e3t + 1)dt. -cos(3rx)

A:

Q: 2 sinºx cos®x dx

A: here we use integration method, as we seen that the power of the sin and cos are even . so we use…

Q: Solve for the differential of y when y- sinax. x= and dx O o o

A:

Q: 4. cos x dy + y(sinx- 1) dx = 0; when x = n, y = -2

A: (4) To find: The solution of differential equation. Given: The differential equation is…

Q: The derivative of : y =0(sin (In (0))) + cos(Im (0)) is:

A:

Q: tan(2x + 2). Find the differential dy when x = Let y : 4 and dx 0.2 Find the differential dy when x…

A:

Q: A-The derivative is y = In Vsin 0 cos 0 1 + 2 ln 0

A: Let's find derivative of given  function.