Differentiate with respect to the independent variable. f(x)= (e^x + cos x)^6 (3x^4 - sin x)^2

Q: Find dy/dx by implicit differentiation   2x3 +x2y  -xy3  = 2

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Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

Q: Find the critical points of the function f(x)=sin2x−cosx on the interval (0,2π).

A: For critical points, first find the derivative of the function and equate it to zero.

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) = tan tan (3x2+2x)( Ans: (6x + 2) sec2 (3x2+2x) solution?

A: Let,

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

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

A: Given that: ∫sinhx.coshx.dx

Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

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

A: Differentiate above equation with respect to x.

Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

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Q: f(x) = e2 sin¯+(3x) + In (cosh-1(e³x))

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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: What is the first derivative of q(x)= ln((7x^2+3x+7)/((x^5/6)(tan(x)))

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

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Q: Find dy/dx by implicit differentiation. 9x3 + x2y - xy3 = 1

A: Given that: 9x3+x2y-xy3=1

Q: #11, find dy/dx by implicit differentiation

A: Differentiate question 11

Q: Compute the higher derivative.

A: Given, d3dx3sin 2x

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

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: Choose the derivative of sin (x). - 1 1 1+ x2 1 x2 | 1 1+ x2 1 xVx2 1 - 1 V1- x?

A: It can easily find the derivative of function

Q: Find the derivative. 5х + 1 In 5x - 1 dx 5x +1 %3D dx 5x -1)

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Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

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

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Q: 2. Integrate using Trig: cos° x dx

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Q: Compute sin x dx er + 3e -x 8.

A: We have to compute the given expression ∫sinxex+3e-xdx from -∞ to ∞ Therefore, The  given expression…

Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

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Q: Find the anti-derivative of: f(3x^3+9x)^6 (x^2+1)dx

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

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Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

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

A: Use implicit differentiation

Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Compute the fourth derivative of cos(x+1) - ln(x²+4) + x²²+1 with respect to x. Also, compute the…

A: Sol:- First part:- Fourth Derivative of given function:-…

Q: Find cosh æ In(sinh x)dx.

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Q: Find the derivative of f(x) = 9 sinh-' (x²) – 9 In ( Vx4 + 1). %3D

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Q: what is the first derivative of cosx^2(x^2+2)

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Q: find dy/dx by implicit differentiation yetan-1 x = 2

A: y·etan-1x=2

Q: find the first derivative of the function. F(x)= (1+sin2x/1-sin2x)^3

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Q: Find the possible values of cosh x that satisfies sinh²x – 3 cosh x + 3 = 0

A: We use the following identity to solve question 1). cosh2x - sinh2x = 1

Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

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Q: Solve for the derivative of the function using chain rule. 14. f(x)= 3lnx 15. f(x)= cos(cosx))

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Q: Determine the first derivative of the ff. function a. y = 400(2)*+3 sin 3x b. y = Vxe2x cosx…

A: Given1) y=400(2)x+3sin3x2) y=xe2xcosx3)y=1+ln(3x2)1+ln(4x)We need to find the first derivative of…

Q: Find dy/dx by implicit differentiation. 3+10xv+4x-5x=0

A: Given

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: by implicit differentiation. 8. Find dx sin(xy) = 1+ cosy,

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Q: Integrate: cos Gx) – sinh(2x)]g

A: As per our guidelines only one question can be answered.Please repost the next part in next…

Q: Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

A: We use the special results of Gamma function to solve this problem as in next step.

Q: Find the derivative of a. (e(sin2x))/[In(cos2x)]2

A: We have to find out derivative

Q: y = sin(3x²) cos(3x²)

A: