The Derivative az/ax of sin(xy+z)-sin(zx- * :y)+sin(yz+x)=1 is -ycos(xy+z)-zcos(zx-y)-cos(yz+x) dz/dx= cos(xy+z)-ycos(zx-y)+ycos(yz+x) Option 1 O ycos(xy+z)+xcos(zx-y)-zcos(yz+x) cos(xy+z)-xcos(zx-y)+cos(yz+x) dz/dx= Option 2 O -ycos(xy+z)+zcos(zx-y)-cos(yz+x) dz/dx= cos(xy+z)-xcos(zx-y)+ycos(yz+x)

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

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Q: Find the Differential of a Composite Function Original function                        y = f(x) =…

A: Applying chain rule we get:

Q: ag Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2/2, 7) where g(x,…

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Q: What is the dy/dx of y = 3sin²x cos x ? O 3 sin x(sin²x - 2cos²x) O-3 sin x(sin²x - 2cos²x) O 3 sin…

A: Given: y=3sin2⁡xcos⁡x To find: dydx We know that ddxcosx = -sinx ; ddxsinx = cosx

Q: az QI. Find the az and ax partial derivative ду x² sin (y*) + xe³ – cos (z) = 3y – 6z + 8

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Q: 26) Find the partial derivative of of f= y cos x+ 2x sin z + 5y with respect to y.

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Q: Solve for dy given xsin y - ycos x = 2 | dx sin y-ysin x А. cOS X-XCOs y sin y+ysin x В. coS X-XCOs…

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Q: Use the derivative rules to write the first step of differentiation. (arctan(x))6 = 6 (arctan(x))5 ·…

A: We will find the first step of differntiation as following

Q: Find the derivative of the function. rsin(x) y = In(1 + 5v) dv y'(x) = sin x In(1+5 cos x) + cos x…

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Q: Find y' by implicit differentiation 1. x²+4x-3y²+4y=0 2. 2xy+π sin y = 2π

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Q: Find y, of (D² + 1)y = sec x = In |cos x| (cos x) - x sin x В y = x sin x + (cos x) In sec x = x sin…

A: Please see the below picture for detailed solution.

Q: Explain of the method of proving the derivative (dy/dx) of y=U(x)ᵛ⁽ˣ⁾ where U(x) and V(x) are…

A: y=uxvx, where ux  &  vx are the differential functions of x. To differentiate these type of…

Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

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Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

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Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i -3j b)…

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Q: Find dy/dx for x⁴+siny=x³y²

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Q: Find the derivative of y = 4) G* eln sin-) y = G (In-x) sin + V4 – x2. x sin¬1 In sin + (Tx-1 1 y' =…

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Q: If f(x, y) = y cos(x) – a° In(y), find the second partial derivative ду дх .A 3x2 = -2y sin(x) ду дх…

A: Option (a) is correct.

Q: Find dyldx y =-secu, u = x- COs X dy -sin(x-cos x) cos x) sin(x-cos x) cos(x - cos x) sec(x- %3D dx…

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Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

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Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

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Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: 1 point) Find dy/dx by implicit differentiation. 2cos(x)sin(2y)=−4 dy/dx=dy/dx

A: It is implicit differentiation.

Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

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Q: What is the derivative of y = tan-1(x2 + 1)? dy dr 2 1+( z²+1)² dy dr /1+(z²+1)² dy O dr V1+(2+1 )°…

A: To find derivative of y=tan-1x2+1

Q: If f(x,y)=3 sin (2x+y)-4 cos (x-y) then the second derivative f , is a. 3 sin (2x+y)+ 4 cos (x-y) b.…

A: In the question it is asked to calculate the double derivative of the function given.

Q: Find the derivative of cos(In(x)) ((x)soɔ)u| cos(In(x)) – In(cos(x)) sin(In(x)) cos²(In(x)) A cos…

A: The objective of the question is find the derivative of the given function.

Q: Find a result by using homogenous for (x³ - 3x²y)dx-(x3³ - y³)dy = 0

A: This question is based on solution of Homogeneous differential equation.

Q: y = Arctan ( sinh (2x)); y' = * O - 2 coshx /(1+ sinh^2 (2x)) O 2 coshx / (1+ sinh^2 (2x)) O 2/ cosh…

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Q: Find dy/dx using appropriate derivative rules. 1. y = 8x^5/2 - 7x-9 + square root of 5 2. ) y =…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

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Q: Find the first derivative of * In (sec y + tan y) - x - sinx = 2 O tany (cos.x + 1) O cos y (cos x +…

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Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are…

A: We have to explain of the method of proving the derivative dydx of y= U(x)V(x) where U(x)and V(x)…

Q: 1-f²₁ ¹/²(y² sinx dx dy) 2-√²-dxx2 0 3- f(cscx cotx)² 2 4- f₁² x (x − 3)dx for 5-S²₂ (x³ + √x) dx

A: 1.

Q: Integral of | 4sinxcos cos |dx 1. J sin 9x cos4x dx J cos 2x cos (-x)dx 2. 3.

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Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: Find the derivative of y = Arccot (tan(esecx)) in its simplest form %3D A. y' = e Sec*secxtanx B. y'…

A: This question is related to differentiation, we will solve it using given information.

Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: Find the derivatives of the f: 1. y: sin (x²+3) 6. y= e tan 3x 7. y: e 2. y= tan (4x*) cot (3x-8) 3.…

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Q: Find the firsst derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and the first partial…

A: Given:       y=arctan3sinx4+5cosx First derivative:     dydx=ddxarctan3sinx4+5cosx…

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

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Q: 5. Integrate: S (cose-sin8) de sec 20 6. Find f(3y – y³)ž(1 – y?)dy

A: 5. Given integral, ∫ecosθ-sinθ2sec2θ

Q: 1. (sin y — y sin x)dx + (сos x + х сos y — у)dy 3 0 %3D 2. (1— 2x2 — 2х) у' %3 4x3 + 4ху 3. (Зx cos…

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Q: Use implicit differentiation with partial derivatives (as described in Example 4 page 732) to find…

A: Given function is, x2y+xy=4

Q: Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2V2, ), where g(x, y) :…

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Q: A curve y = /(x) have length of the curve from x 0 to x= n/2. dy Vcos(2x - 2) as its first…

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Q: Obtain the particular solution. 1. 2y dx = 3x dy ; when x = 2 , y = -1 .

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