Using partial derivatives, which one is equivalent to dz/dt, given z = x² + 3xy + 5y2; x = sin t, y = cost? O (2x + 3y)cos t+ (3x + 10y)sin t O (2x + 3y)sint+ (3x + 10y)cos t O (2x + 3y)sin t-(3x+10y)cos t O (2x + 3y)cos t-(3x+10y)sin t

Q: d Evaluate the following derivative: dx (1 + t² dt. Oxv1 +x4 + v1+x² Main Content None of these O…

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Q: Differentiate y = Væ + Vx + Væ. y =

A: We need to differentiate the given y with respect to x

Q: Step 3 Now write the derivative in terms of x by recalling that u = -3x + 7 and v = x + 7. du 1 +=…

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Q: 2) Find the derivatives of a) y = 7 - 6x-x² b) y - ³x 8 √x

A: Given :(a)y=7-6x-x2(b)y=-8x

Q: Find the derivative of f(w)= sin(4w²)+cos(4w²). A) Swcos(4w°)–8wsin(4w²) B) -8wcos(4w?)+8wsin(4w²)…

A: Given function is  f(w)=sin(4w2)+cos(4w2)Derivative of f with respect to w:f'(w)=…

Q: Find the derivative of y with respect to s. y= sec 1(7s° + 4)

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Q: Find the derivative of y with respect to x for y= ( cos 7x) ot /X Choose the correct derivative of y…

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Q: sinx

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Q: Calculate the derivative of 2t – 1 > t + 2 r(t) =< 3t – 5, 2t2 + 5t + 7,

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Q: Recall the derivatives of some common functions, and complete the table below Function Derivative…

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Q: sin x 8x y = 8x sin x dy 8. CoS X 8. %3D dx cos X dy dx x cosx + sin x 8 sin x + 8x cosx 8x2 sin2x…

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Q: x2 – y? + xy = x²y Find dyldx using implicit differentiation.* 2ху-2х-у x-2y-x2 2ху-у x-2y+x² >>…

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Q: y-Castesinz şinz

A: The detailed solution is as follows below:

Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

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Q: Q1) Find the first derivative of the following equations: y = x'V

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Q: Find the directional derivative of f (x,y)=2x² cos 2y at 2, in the direction of 3i+4j. 2 8 (a)- 5 8…

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Q: Find all second order derivatives for z = 7ye5x Zxx Zyy = Zxy=Zyx = |

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Q: EX/ Find dy for function y = sin ³x + cos³x dx H.W Aus=3sinex (Sinx-Cox) 2

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?

Q: Use implicit differentiation to find y cos (1) = 5x + 5y dy dx

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Q: ind the derivative of y with respect to x. y =-cos-16x + 7° 6 6. 1 + (6x + 7)2 81 - (6x + 7)2 O 4.…

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Q: Find the derivative of y with respect to x if y = (10x- 20x + 20) ex. %3D dy dx

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Q: Find the derivative of y=x√x + 1. 1 dy = 2(x+1) ³ + √² ž √x+1 dy dx = dy dx dy √x+1+ dx = x √x+1 = =…

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Q: Compute Te where f(x,y) = sin(x + y) using the definition the derivative. You need to use sin(a + b)…

A: We have to find