1. Given r(t) = (1+ 2t, t², 3 – t2), calculate r'(t) and T(t).

Q: Let z = x3 y2 ,x=t3, y=t+3 Use the chain rule to find dz at t=3 dt

A: By chain rule of partial derivatives,     dzdt=∂z∂xdxdt+∂z∂ydydt Here we have,       z=x3y2,   x=t3…

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

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Q: Let g(x,y)=ye-3x, x(t) =ln(t2+1), and y(t) =√t Find g(x(t), y(t))

A: To find: The value of gxt,yt. Given: The functions are gx,y=ye-3x, xt=lnt2+1 and yt=t. Concept used:…

Q: t+1 and y = t2 - 2t + 3, then find t-1 dy If x = dx 1 A t- 1 1 B (t – 1)2 1 C (t – 1)² D -(t – 1)3

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Q: dw Use an appropriate form of the chain rule to find dt = In(10x² – 2y + l2³); x = tỉ, y = tỉ, z =t?…

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Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

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Q: х у? dy 1+ y6 ytx dt + t + t3 + (1 – z³)2 ( xy z? dz

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Consider the function T = xe3x+y? dy 5 and dt where x = Vt + 1, and when t O we have y -2. dT when…

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Q: dz 11. If z = e",x=tcost, y =t sin t, compute at t = dt 2

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: dw Use an appropriate form of the chain rule to find dt w = In(162? – 4y + 3z³); 1 = ti, y = tỉ,…

A: Topic- differentiation

Q: ds if s = In [t*(t² – 1)]| dt 20. Find

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Q: dw where w = cos 8x sin 3y, x=- dt 5. and y=t". Use the Chain Rule to find 2

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Q: 1 use the formula L = dt to find the length of the curve dt dt 1 X = y = t° for 0st s1

A: according to the guideline, we are allowed to answer the only the first question  please repost…

Q: dw Find dt if w = xy? + x²z+yz², x = t², y = 2t, and z = 2. %3D t=1

A: In this question we have to find the the differentiation of w with respect to w.

Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

Q: dz Suppose that z = x³ – 3y?, x = 4(t³ – 1), and y = Int. Find using the Chain Rule. dt %3D -

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Q: dz Use an appropriate form of the chain rule to find dt z = 8x"y³; x = t°, y = t Enter the answer in…

A: Topic :- Differentiation

Q: if x²+y²=t-- and x*+y*=t*+=,prove dy X t dx 3. ху

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Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

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Q: 3. Let X(t) = t2W (t) – 2 f sW(s)ds, Is X(t) a martingale?

A: X(t)=t2W(t)-2∫0tsW(s)dsWe know that, X(t) is a martingale, if,EX(t+1)=X(t)

Q: Q6. If w = y²z² + xy and x = t³ – 1; y=t² + 2; z= 3t , find the total dw at t = 2 dt differential

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Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

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

Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: b. g(x) = [ cos(r*)dt x²+5x F(x)= [,(6r* +6e° )dt с. 6t +6e" dt

A: We have to find derivative

Q: dy t² +3 21. Find 9 if y = In dt /1-t,

A: We need to find derivative of given function with respect to t

Q: dw Use the Chain Rule to find dt w = x²e²y cos(32), x = cos t, y = In (t + 2), z = t

A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x).

Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using…

A: The given function is w=8x2+3y2, x=cost and y=sint. We have to express dwdt as a function of t.…

Q: Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

A: Let's find.

Q: dw if: dt Q1) Using the chain Rule to find w = xy + 3z, x = sint, y 2 cost, z=t (x2 +)

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Q: dz Use an appropriate form of the chain rule to find dt z = 4x°y³; x = tº, y = t" Enter the answer…

A: From the given problem: z=4x6y3 ; x=t8 , y=t7 Now apply the chain rule.…

Q: Q) Compute for y(x) sec (2x) + 2x -1 and x(t) = 4cos(t) at t-1

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Q: dw Find if w = xy? + x²z+yz?, x = t², y = 2t, and z = 2. %3D dt |t=1

A: Simple derivative problem....

Q: Let y(t) satisfies dy 3ty-t-t for t20, dt 1+t2 and y(t 0) 1. Show that y(t) S1+t² for t2 0.

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Q: Let z(x, y) 2x2 – 3y? where a 2s – 4t & y = 9s + 8t. he at dy dx az Calculate ds dz by first finding…

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Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: Use an appropriate form of the chain rule to find dz/dt 1. 2 3xy; a r-t' and y

A: use partial derivative for finding drivative.

Q: 2. Find dy where y = v3x3 +4x + 1.

A: Given y=3x3+4x+1

Q: Given f(x, y) = 8x²y then the total differential df ,2, O 8xy dx + 8x² dy O 16xy dx + 8x² dy O 16x…

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Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

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Q: S(t)e¬Jwnt dt_ 2 C =

A: In this question, we find the coefficient for the Fourier complex series cn=2T∫0Ts(t)e-jwntdt

Q: If w= 2e*_lnx find dw/dt , x=In(t^2 +1), y=tan t, z=e^t

A: If w= 2ex lnx Find dw/dt, x=ln(t2+1) dw / dt = [ ∂w/∂x ]  [ dx/dt] + [ ∂w/∂y ]  [ dy/dt]…

Q: IF V = xsin(y) + ye where x = s + 2t and Y = st Use the chain rule to find dv and- ds dt when s=0…

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Q: dw Evaluate at the given value of t, by using the Chain Rule, dt w = 2ye* - Inz, x = ln(t² + 1), y =…

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Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: If x=t² - 5t and y=1-61 , then dy at t=1 is dx

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Q: If z = e* sin y, where x = s?t2 and y = s²t, by using Chain Rule find ôz/ðs and az/dt.

A: Let's find.

Q: ) Find dw if w = xe³/², x = t², y = 1 — t, and z = dt 1 + 2t.

A: Topic:- application of derivatives

Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

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