Find vf(x, y) if f(x,y) = e* c cos y 5.

Q: Q3) for f(v) = sec2(3v – 1) and g(v) = tan?(3v – 1) show that %3D %3! f'(v) = g'(v).

A:

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

Q: Get z = f (x,y), x= e° cos t, y = es sin t Show that it's + ) - 2 2 =e 2s + əx. əs

A:

Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

A:

Q: Determine when the following pairs of functions are linearly independent. (a) y1(t) = e"it; Y2(t) =…

A:

Q: 8. For the function y = e* + sinx: a. Determine y', y",y",y^),y(5), y(6). b. Describe the pattern…

A: We have to find the differentiations of the give function and find y101.

Q: Let f(x, y, 2) =x² + 3r°y? + 2°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

A:

Q: Find fxxx for f(x, y) = Sin() at (π, π)

A:

Q: For f(x1, x2) = x2 cos x1 find f'(x1, x2), f'(2,7) and df[(2,7); h]. For f(x, y, z) = (x – 2z)e"…

A:

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

A:

Q: Find f. f(t) =|| f"(t) - 3et+ 5 sin t, f(0) = 0, f(T) = 0

A: To find f.f''t=3et+5 sin t, f0=0, fπ=0

Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: 2. Given f(x,y)=xy°e*: (a) Find the first derivative f,(x,y). (b) Find the first derivative f,(x,y).…

A:

Q: Given a function f(x, y, z) = cos (x + xy²z²), find: f#(5,1, 1) = frz (T, 1, 1) = %3D

A:

Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

A:

Q: Find f. f"(t) = 5et + 4 sin t, f(0) = 0, f(1T) = 0 f(t)

A: topic- differential equation

Q: Q3) for f(v) = sec2 (3v-1) and g(v) = tan2(3v- 1) show that %3D S(v) = g'(v).

A:

Q: Given f(x, y) = e²y (xy + x), show that fyy(x, y)-xfy(x, y) = x²e²y.

A: fy  denotes partial first derivative wrt y.  fyy denotes partial second derivative wrt y