Find (x*sin (2))'.

Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos…

A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 .

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

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Q: Integrate sin^2(7x)-cos(x)

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Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

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 g(x) = In(sin²(ed/x)).

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Q: 7. Find the derivatives of y = cos- (sin(2x)) (show work)

A: Using derivatives of composite function. Or Using trigonometric transformation.

Q: Use implicit differentiation to find: (sin3.14x+cos3.14y)2=2

A: Consider the given equation.

Q: 2 Find the derivative of: – 8 sin (3x°).

A: The chain rule of derivative states that ddx(f(g(x)))=f'(g(x))g'(x). The power rule of derivative…

Q: Solve using implicit differentiation.    y cos x = x2 - y2

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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: Express in exact form: In(x² + 1)dx

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

A: Given that y=cos6θ+15 Find dydθ Needed formulae: xn'=nxn-1 cos x'=-sin x ax'=a

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos4…

A: Given: y=cos4θ

Q: Use the first principles to find the derivative of cos(x -4x).

A: By the first principle  f'(x)=limh→0f(x+h)-f(x)h. So, dcosx2-4xdx=limh→0cosx+h2-4x+h-cosx2-4xh…

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

A: We have to find derivative

Q: If y- sinhx then prove that = dx

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

Q: Compute the derivative. k(θ) = θ2 sin2 θ

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: What is the derivative of y = sin(3x²) cos(3x²)

A: We have to find the derivative of given function.

Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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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: Find the derivative of cos-¹(sin x)

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Q: Find the 75th derivative of y=cos(2x)

A: Given function y=cos2x The 75th derivative has to be founded  first consider the smaller…

Q: Find the derivative of the function.

A: The given function is y=ln5sinx

Q: The derivatives of sin- 1 x and cos- 1 x are negatives of each other.

A: From the question it's not clear, what do you want us to do with it. I assume that you want to know…

Q: find integral sin 5 x  cos 2  x dx

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Q: Find the derivative of the function f(x) = at sin(7x + 14) + In(2r+10)

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

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Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos4…

A: Using chain rule to compute the derivative for y, consider the solution below.   First of all,…

Q: Evaluate integral sin^4(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: g(x)%3Dx sin(2*)

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Q: sinx In (2) co cos x

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

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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: Use differentials to estimate sin (π/6 + 0.01).

A: Use differentials to approximate the value of sinπ6+0.01 The nearest number to sinπ6+0.01 whose sine…

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

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Q: Find the derivative. y = In(x²)tan (3x) %3D

A: Given:

Q: Find the second derivative y=lnx + 3 sin(4x) d²y dx² of

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

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Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: Find the derivative of y = /sin (7x + In(5x)) %3D

A: Here we have to find derivative of given function.

Q: 14. y = In cos 4x

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 6x 2) = 4 y7

A: 2) Given- 6xy7=4 To find- The derivative of the above expression using implict differentiation.

Q: x sin 2x sin cos x 2 X. Prove that 8 dx 2х - л

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

A: We have to find out derivative