prove that (d/(dx))(sec^-1x)=1/(xsqrt(x^2-1))

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: On which derivative rule is integration by parts based?

A: Integration by parts is based on product rule of derivative. Mathematically, Product rule of…

Q: show how to use integration byparts to find integration (arcsin x)^2 dx

A: Let I=Arcsin x2 This can also be written as: I=sin-1x2 Now if we want to integrate above function we…

Q: What is the resulting integrable form after you applied substitution technique in tanx sec“x dx?

A:

Q: Verify Eq. (2): cosh2 x - sinh2 x = l.

A: To verify Eq. (2): cosh2 x - sinh2 x = l.

Q: Use implicit differentiation to find * az given that yz* + x²z3 = дх = exyz

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Q: Integrate: S tan (æ) sec³(x)dx

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Q: Find the derivative of f(2) = sinh(2²) – 2z cos(32). Is this an analytic functio %3D

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Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: To calculate the integral

Q: Use Leibniz’s Rule to find the derivatives of the functions

A:

Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: We write the expression using exponent and then integrate C=integrating constant

Q: integral of sin^5(3x)cos^3(3x)dx

A: The integral of ∫sin5(3x) cos3(3x) dx is sin5(3x) cos3(3x). If we need to find the integration then…

Q: Tangent line of ex+ey-2xy = 2(e-1) at point (1,1) using implicit differentiation:

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Q: Using implicit differentiation, what is the value of dy/dx in 4x-x²y+y³ = 10 at point (1,1)?

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Q: integral of 1/sin3x dx

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Q: Find the derivatives of the functions in Exercis

A: Given function is: y=1x sin-5 x-x3 cos3 x We have to find dydx.

Q: Xyz. %3D Use implicit differentiation to find az/ar

A: The given function is ez=xyz.

Q: What are the formulas for differentiation and intergration? When to use them?

A: Query- What are the formulas for differentiation and intergration and describe When to use them?…

Q: %3D

A: Solving

Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

A:

Q: Find the derivatives of the functions in Exercis

A: fθ=sinθ1+cosθ2

Q: Find the derivatives of the functions in Exercis

A: we have to find the derivative of the given function. g(t)=1+sin3t3-2t-1

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

A:

Q: Which derivative rule is used to derive the Integration by Parts formula?

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Q: Find ∫cosh 2x sinh2 2x dx.

A: To find the value of the integral∫cosh2xsinh22xdx

Q: 1+ tanx y = logy 1- tanx prove that 9 = sec2x dy dx

A: Given,           y=log1+tanx1-tanx

Q: 2. у %3D 3 + 4x — х?

A: We can find the answer as below

Q: find integral sec 3 x dx

A:

Q: integral sec2(?) tan2(?) d?

A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c

Q: Find first and 2nd derivative guncic 2 tan2x 3.

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

Q: rIn 2 cosh x dx. Vsinh a x + 4 sinh x +2

A:

Q: The second derivative of y = ln(sec x) is а) у 1 - tan x b) y = tanx sec x c) y = secx · tan x d) y"…

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Q: Find by implicit differentiation when ry sec(y) 1+y* 3 -

A: The given equation is:xy3secy-3=1+y4

Q: Find the equation of line tangent of sin(2x) cos(3x)+ sec(x) TC At x = 6. %3D

A:

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: у %3DIn(In sec x)

A:

Q: Find:  ∫cosh^4 (x) sinh^5 (x) dx.

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Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

Q: dy Use implicit differentiation to determine given: 2x3 + x²y – xy3 = 5 - dx

A: Given, 2x3+x2y-xy3 = 5  We have to find dydx

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

A:

Q: Calculate the derivative: d/dt ∫ from 1 to tan(t) of sin(x^2)dx=

A: Here the function is of the form:

Q: Integrate f sinh 2x dx

A: In this question we have to find Integration.

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: Integrate (tanx)^3(secx)^3

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Q: (7 – siny)y' = 3x2 + 2x

A:

Q: Find the fifth derivative using product rule y = sin3xcos4x Where r is the last digit of your…

A: The fifth derivative of the given function can be found by differentiating the given function five…

Q: Jcos" (3x) sin (3x)dx in' (3x)dr

A: topic - integration

Q: Use implicit differentiation by partial derivative to solve for dx of function 3x2 + 2xy = -4y3. %3D

A: