Evaluate and simplify y'. y = V1 - x* + x² sin-'x?

Q: sinh³ (x) cosh (x) dx =

A: we have to evaluate the integral ∫sinh3x cosh8xdx use the formulas,…

Q: 10) y = xtanx + sin-ly

A: according to guidelines we should able to do only one question at a time #10

Q: Differentiate the function. y= ln(x3 sin2 x)

A: First, we simplify the given function using the multiplication and power rule of logarithm.

Q: 2. y = (cosx)(sin5x)

A: We will use product rule of differentiation to find the first derivative of this function. We will…

Q: Find the first derivative of  y = (x – 1) √ (2x – x2)   + arcsin (x – 1), and y = arctan [ (3 sin x)…

A:

Q: Evaluate S sinh x cosh x dx by introducing u-sinh x

A: Given that: ∫sinhx.coshx.dx

Q: Compute the derivative. y = sin (4 / θ )

A: The chain rule of differentiation is used to find the derivative of a composite function and given…

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = (2…

A: Given function is   Differentiating both sides with respect to x, we get

Q: 6. Find dy/dx by implicit differentiation for tan-'(²y) = sin(x²) + 3ry?.

A:

Q: compute the derivative y = sin(2x) cos2 x

A: Given y=sin(2x)cos2x The product rule of derivative is given by:

Q: 1) Find 4 by implicit differentiation given 4 cos x sin y = 1. dx

A: Differentiate above equation with respect to x.

Q: Find the first derivative y = (cosx)(sin5x)

A: Answer and explanation is given below

Q: 4х — бу? 3 ху?

A:

Q: find the derivative.

A:

Q: Find the differential of the function y = x- sin x.

A: Given: y=x2-sinx

Q: Find the differential of z = sin²(5x) + ev

A:

Q: Find the coordinates of the point on the graph of y = 8 sin x+4 cos (2x) + 14, 0 <x<5, where the…

A: Consider the given function, y=8sinx+4cos2x+14 The slope of the tangent line on the given curve will…

Q: Find the indicated nth derivative of the following: 1 7. 2nd derivative of y = xArcsinx + v1 – x²…

A: Find derivative using product rule and composition of functions rule

Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: Evaluate S sinh x cosh x dx by letting u=cosh x

A:

Q: 1. Differentiate the function. y = In(VT sin-(5æ))

A: As per our guide lines we can answer only 1 question. Kindly post the other question seperately.…

Q: Evaluate: S Arctan 2 sin²x dx . Arctan 1 cos+x

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: Find the derivative of ,In sin-1) y = e %3D

A:

Q: Calculate the derivative. y = (In (cosh(x)))° (Use symbolic notation and fractions where needed.) dy…

A:

Q: Compute coshx and tanhx, assuming that sinhx = 0.8.

A:

Q: 1. cos(xy) + secy = 5

A: Differentiation is the process of determining the derivative also known as the derived function. one…

Q: find the root of 3x +sinx -e ^x=0 using secant method

A: Let us consider the function fx=3x+sinx-ex. We have to use the secant method to find the…

Q: 4. Use implicit differentiation to find dy when 3x? - 2y = xy dx

A: Given: The equation, 3x2-2y2=xy.

Q: 2.Find , if y = sinh x %3D dx' 1+cosh x

A:

Q: Differentiate the function y=ln(x5 sin2 x)

A:

Q: The nth derivative of y = sinx cosx

A: We know that,  2sinxcosx=sin2x Therefore, y=sinxcosxy=122sinxcosxy=12sin2x              ⋯⋯1…

Q: 4) 8х — у? %3D 3

A: Consider the provided equation, 8x-y2=3 Find the y' by implicit differentiation.

Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: 8. The value of f sinh* x cosh³ x dx

A:

Q: 3- - 플 플 sin²cyl y จน

A:

Q: Differentiate with respect to x. Y=sin5x

A:

Q: Find az when yz+x In y = 2.

A: Use implicit differentiation

Q: sinx In (2) co cos x

A:

Q: Find:  ∫cosh^4 (x) sinh^5 (x) dx.

A:

Q: 1 3), sinh(x)-cosh(x) dx

A:

Q: Find the differential for y = tan 2x2

A: Find the differential equation for given equation We need to take derivative for tan using the…

Q: Find y' by implicit differentiation: 8 cos(ry) + x4 = yª

A: Given: 8cosxy+x4=y4 For finding derivative of given expression, we differentiate given expression…

Q: differentiate the function: y= ln(x^9 sin^2(x)) y'(x)=

A: Given function as

Q: Find the derivative of y=x?sinx x?cosx +2xsin x 2xcos x x2 sin x+2xcos x x2cosx

A:

Q: Which is the derivative of y= sin (x2-2x + 1)? О 2х-2) (2x-2)Cos(x²-2x + 1) O Option 2

A:

Q: 4. Use implicit differentiation to find az in xexyz sin(2z) – xyz = 5. ду

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 3. Find if y³ + 2xy - x² = cos x using implicit differentiation.

A:

Q: Compute the derivative of h(sin(x)) at x = * assuming that h' (u)lu=0,5 = 10. (Use symbolic notation…

A:

Q: Solve for the derivative of the Trigonometric Differentiation. 1. y = sin (5x) + 3x cos (5x) 2. y…

A: given y=sin5x+3cos5xdiffrentiate w.r.t. xdydx=ddxsin5x+3cos5xdydx=ddx(sin5x)+ddx(3cos5x)we know that…

Q: Se Sin (3x) dx by Improper htegrations.

A: use improper integral