Find F'(x) given that F(x) 3+sin (5t) dt. |3D In (t8) Provide your answer below: F'(x) =

Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: If x+y divided by x-y= x^2+y^2 and dx/dt=12, then what is dy/dt when x=1 and y=0? show all work…

A: Given thatx+yx-y=x2+y2x+y=(x-y)(x2+y2)  [cross multiply]x+y=x3+xy2-x2y-y3

Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

Q: Find dy/dx by implicit differentiation   4Cos x Siny  =1

A:

Q: Find the anti-derivatives, using ONLY basic rules + 3* ) dx

A: Note:- We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: (2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

A: We know that if - M(dy/dx)+N=0 Then M(dy/dx)= -N Therefore- dy/dx= -(N/M)

Q: find dy/dx by implicit differentiation. 3cos(8x)sin(7y)=8

A:

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

A: The given function is 3y+9x=1

Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: Determine the anti-derivative of Y = 2e3x +5 and use the fact that y(0) = 7 to %3D dx determine c,…

A: We first separate the variables and then integrate  c= integrating constant Formula used:

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

A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

A:

Q: What is the derivative 7 of y = (3x + 1)²? 21 dx dy = 6 (3x + 1)²¹ dx = dy 6 (3x + 1)² dx = 7 (3x +…

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Q: tan (2x + 3). Find the differential dy when x = 3 and dx Let y = Find the differential dy when 3 and…

A:

Q: in integrating the function fx cos() dx using intogration by parts, whut would you choose for your…

A: Solution

Q: dy Find by implicit differentiation. 20x = 20 - ey ... dx (Type an exact answer.)

A:

Q: Compute the differential dy  for  y=(6x+sinx)^3

A:

Q: tan(3x + 8). Let y : Find the differential dy when x = 5 and dx = 0.4 Find the differential dy when…

A:

Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: The position of a particle moving along the x-axis is x(t)  = sin(2t) - cos(3t) for time t>= 0. When…

A: Given the position function, x(t)=sin2t-cos3t

Q: Find dy/dx by implicit differentiation. 3 cos (9r) sin (2y) = 8 dy/dx =

A:

Q: Find dy/dx by implicit differentiation. 6,,3 x°y - y = x dy/dx

A: On implicit differentiation we differentiate both sides of the equation with respect to x . Then we…

Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: I. Find an equation of the tangent line to the graph of 1 t cosh (t² – 1) dt - f (x) = 1 tan-t 1+ln…

A: The given function is fx=∫1+lnx1tcosht2-1tan-1t dt.

Q: Find the derivative of F(x) = 4 n sin(t) dt. %3D dx 3x² cos(x)

A: Integral calculus is one of the two main parts of calculus that is concerned with the study of…

Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

Q: Calculate the derivative d In (t)dt dx Ja4 using Part 2 of the Fundamental Theorem of Calculus.…

A:

Q: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

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 fx cos(3x) dx using integration by parts, what would you choose for your…

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the…

Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

A:

Q: y= sinh-lx then prove that Vx2+1 dx

A:

Q: find dy/dx of y=sin^2 4x+1/2 cos 8x

A: Given,         y=sin24x+12cos8x

Q: Find the slope of the tangent line to the graph of f(x) = x· 2e*cos-1t dt at x = 1 Jln x

A:

Q: Find partial derivative af for the function f(x,y) given below exp 2x. siny .(at the point (In2, 0

A:

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: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: dy Obtain general solution of- 3/xy dx

A:

Q: Find the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

Q: Find the derivative. cos X d 78° dt dx 1 a. by evaluating the integral and differentiating the…

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Q: -Find for: y= sinV1-t dx

A: We have to find dydx for y=sin-11-x4.

Q: of (xy + 3)5 = 2x – 2y³ + 19. dy Use implicit differentiation to find dx

A:

Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

Q: Find dy/dx by implicit differentiation. 5x^(3)+x^(2)y-xy^(3)=-8 dy/dx=?

A: We are given an implicit equation as

Q: 5. Find dy/dx using implicit differentiation given x²y³ + cos y = 0.

A: Definition used -  Implicit differentiation -     It is a rule by which we can find the derivative…