Let z(x, y) = x°y where a = t & y = tª. dz Calculate dt chain rule. dx by first finding dt dy and using the dt da 8t7 dt dy 4t3 dt Now use the chain rule to calculate the following: dz dt || ||

Q: dy Assume x and y are functions of t. Evaluate for the following. dt y²-9x³ = -31; dx dt = -6, x=2,…

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Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: 1. Explain why / f'(t) dt = f(b) – f (a). ||

A: Refer to image below.

Q: Express dm/dt as a function of t and evaluate dm/dt at given point where m = z- sinxy, x=t, y=lnt,…

A: Given m=z−sinxy, x=t, y=lnt and z=et−1 We have to find the dmdt Use chain rule…

Q: Let xy = 4 and dx dt Find dy dt when x = = 2. 1.

A: ..........(i)Differentiating equation with respect to t Put   ..........(ii)

Q: da at I = –1if y = – 1² + 2 and dt dy dt 2. Find da dt

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Q: (c) Differentiate y = Vsec3 (5t2)

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Q: dy Find the derivatives dx of the following functions csin x Vt2 + 1 dt 2

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Q: Find the interval on which the curve dt 3 +t + 212 y = is concave upward.

A: Given: y=∫1x13+t+2t2dt

Q: dy dx Given y=x³ - 2× and = 3. Determine the value of dt when X=2. dt

A: Differentiate the equation y=x3-2x with respect to t. y=x3-2xdydt=3x2dxdt-2dxdt=3x2-2dxdt

Q: dz Q2: Let z = x?y, x = t2, y = t3. Calculate by (a) the chain rule, (b) expressing z as a function…

A: Given: z=x2y, x=t2, y=t3 For finding dzdt by using chain rule, we differentiate given expression…

Q: z = sin x cos y, = VE, y = 1/t x =

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Q: For the function f(x, y) = (cos x)ey +v 1 + x + y. %3D Show the process of using the linearization…

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Q: Find tan(t² + 5)dt. dx

A: To Find:

Q: dx at x = dt dy - 22 – 2 and dt – 5 if y = 4. Find - dx dt

A: We will find the derivative.

Q: a) = 2, giving your answer to 2 decimal places if Find the gradient of the curve y at the point a…

A: Given function  Gradient of function y is given as follows

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: Given t = x + ex, find dx/dt

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Q: If fo f(t)dt = 2, So f(t)dt = -6, and f(t)dt = 1, find i f(t)dt.

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Q: Differentiate the function y = 6 + x using the Chain Rule. dy %3D

A: Given, the function is                              We have to differentiate this function using…

Q: dw Jse the chain rule to find dt where w-x+y,x sint + cost y = cost- sint.

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Q: z = 5x+ 4y subject to: 4x -ys 16 3x +y2 13 x23 Use graphical methods to solve this linear…

A: To solve the linear programming problem using the graphical method first, convert the inequalities…