Let f(x) = 6 sin (a*) f'(x) = NOTE: The webwork system will accept arcsin(x) or sin-(x) as the inverse of sin(x).

Q: Find the first derivative of y=x arcsin x + √1-x²

A: y=x arcsinx+1-x2

Q: Compute the derivative arctan(x)arcsin(x)

A: Given: arctanxarcsinx

Q: (5x) S sin(x) tan(x) .........

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Q: Find the derivative of f(x) = arccos 3x + arcsin 3x.

A: derivative of arccos(x)=-11-x2 and derivative of arcsin(x)=11-x2

Q: Let y=sin2x. Differentiate this function without using the chain rule.

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Q: Find the 1st derivative y=(x-1V2x-x t arcsin (x-1)

A: I am attaching image so that you understand each and every step.

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: Find the derivative of f (x) = arccos 3x +arcsin 3x.

A: Given: f(x)= arccos 3x+arcsin 3x To find: Derivative of f(x)=df/dx=??

Q: Describe the method used to integrate sin² x.

A: The process to find the integration of sin3x is to write in a way through which its differential can…

Q: How do I verify d/dx(cos^-1(x))=-1/(sqrt(1-x^2)) using implicite differentiation?

A: Verify the result by implicit differentiation as follows.

Q: Va2 -x2 y=Arcsin + 6. X

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Q: Describe the method used to integrate sin3 x.

A: Given I = ∫sin3x dxTo integrate sin3x , substitute sin3x  = sinx . sin2xor sin3x = sinx . sin2x =…

Q: Find the derivatives of the function f(x) from the first principle  sin2x

A: Answer and explanation is given below...

Q: Note that 7 cos(x) In(x) is a product. Therefore, its derivative is given by (7 cos(x)) (In(x))

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Q: What do the limits lim h-->0 ((sin h)/h) and lim h-->0 ((cos h - 1)/h) have to do with the…

A: Show the expression for derivative of sinx0  as follows:

Q: The derivative of sec2 2x(cos2x−sin2x) with respect to x is

A: Given: f(x)=sec2 2x(cos2x−sin2x)   Simplify the function before finding the derivative: By  the…

Q: Determine the derivative of the function y=arcsin 2x / 1+x2 at x=2.

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Q: Calculate the derivative of: cos-(8x) sin-(8x) f(x) f'(x) = 8|

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Q: Show that (x ln(x)) ‘ = 1 + ln(x) using the Product Rule for Differentiation.

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Q: What is the derivative of: y = arcsin(cos x2)

A: Our Aim is to calculate the derivative of y=sin-1cos x2-(i)

Q: tan (5x) x sin3 (2x) 2)- limx-o:

A: we have to evaluate the A=limx→0tan4(5x)xsin3(2x)

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: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: Find the derivative of the function.

A: fx=arc sinx + arc cosx

Q: FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 1. y = Arcsin(- +4

A: Given,y=sinxx2+4sin y=xx2+4cos y y'=x2+4-x×2x2x2+4x2+4y'=sec y1x2+41/2-x2x2+43/2

Q: Find the derivatives of Inverse trigonometric y = arctan (1+4x) у 3 arcsin (1-2x) у 3 arccos V1 -х

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Q: Use logarithmic differentiation to find the derivative of the function. y = (sin 3x)In x sin()…

A: Formula used:If (x) and g(x) are two differentiable functions, then following rules  are efined as;

Q: Is it true that the derivative of y=arcsin(cos2x) is -2?

A: The function is y=arcsincos2x.   Differentiate the function with respect to x.…

Q: Find the derivative of the function f(x) = arcsin x + arccos x

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

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Q: Verify the identity. sinh2 x = (−1 + cosh 2x) /2

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Q: Prove the identity arcsinhx=ln(x+√1+x2).

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Q: Determine the second derivative of the function y=arcsinx2−1x2+1.

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Q: find the derivative. y = arcsin(ex )

A: Given expression

Q: Find the derivative of the inverse hyperbolic sine function y=arcsinh x.

A: Let the given function

Q: Determine the first derivative of the ff. function y = arcsin sin (4x²)

A: Given that y=arcsin sin4x2 To find the first derivative: ddxarcsin sin4x2=11-sin24x2·ddxsin4x2…

Q: find the derivative of this inverse hyperbolic function f(x) = cosx tanh-1(sinx)

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Q: Using the Chain Rule, compute the first derivative of sin 1–x.

A: chain rule Let f(x) = g(h(x)) And let u = h(x) Using the above, function f may be written as: f(x) =…

Q: Determine the second derivative of the function y=arcsin x2−1 / x2+1.

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Q: 1. y= ArctanB %3D 3-V9-x2

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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: Va2-x² Y=Arc sin- + а

A: Solution-

Q: Find Dxy using IMPLICIT DIFFERENTIATION

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Q: Find the derivative of  f(x) = sin(arcsin x) / arctanx

A: Let u=sin(arcsinx)u'=cos(arcsinx)ddx(arcsinx)u'=cos(arcsinx)11-x2u'=cos(arcsinx)1-x2Let…

Q: What is the derivative OF a Arcsin X y= 3

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Q: v = Arcsin(3u2)

A: Solve for the derivative

Q: s(w) = In( w - %3D

A:

Q: What is the derivative of: y = x√arcsin x

A: