use the chain rule to find dz/ds and dz/dt. z=arcsin(x-y), x=s^2+t^2, y=2-6st. dz/ds=? dz/dt=?
57. Find the total derivative dz/dt, given (a) z = x^2− 8xy − y^3 , where x = 3t and y = 1 − t. (b) z = f(x, y, t), where x = a + bt, and y = c + k
Use the Chain Rule to find dz/dt. (Enter your answer only in terms of t.) z = sin(x + 9y), x = 5t6, y = 3/t dz/dt = ? Use the Chain Rule to find dz/dt. (Enter your answer only in terms of t.) z = sin(x + 9), x = 5t6, y = 3/t dz/dt =
Use the Chain Rule to find dz/dt. z = sin(x) cos(y), x= VE, y = 7/t dz dt 11
If z=sin(x/y) , x=3t , y=5−t^2 dz/dt using the chain rule. Assume the variables are restricted to domains on which the functions are defined. dz/dt=
17. A particular solution of X' -(?)x+( 1 ) Select the correct answer. t/4 + 19/16 -t/2 + 7/8 -1/2 + 7/8 1/4+1/8 t/4-1/8 (e) none of the above 20. A particular solution of X' = 2 3 2 1 x+(**): Select the correct answer. 2te/5 + 3e (b) 2te-/5 +3e- - 2te-/5+2e-4 2te-/5-3e- - 2te-/5-2e- 2te/5 - 3e' (c) (e) none of the above
Find dz d given: z = xeyy, x = = to, y= – 2 + 2t dz dt Your answer should only involve the variable t. Let z(x, y) = xºy where x = tº & y = +8. Calculate dz by first finding dt dx -& dt dy and using the chain rule. dt dx d = dy dt Now use the chain rule to calculate the following: dz dt
9. (a) Let Ao(x) = / (1-t*)dt, Ai(z) = / (1-t2) dt, and A2(z) = / (1-t2)dt. Compute these explicitly in terms ofェusing Part 2 of the Fundamental Theorem of Calculus. b) Over the interval [0,2], use your answers in part (a) to sketch the graphs of y Ao(x), y A1(x), and y A2(x) on the same set of axes. (c) How are the three graphs in part (a) related to each other? In particular, what does Part 1 of...
Find the derrivative bellow dz (a) Suppose z = f(x,y) = xexy. Compute if x(t) if x(t) = f and y(t) = +-1.
Problem (4) Let f(z) denote the function e a f(z) 1 - z Compute f (z) dz where y is any contour that encloses the origin but does not enclose the point z =1 Problem (4) Let f(z) denote the function e a f(z) 1 - z Compute f (z) dz where y is any contour that encloses the origin but does not enclose the point z =1