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- 8. Find directional derivative of functionz = xe3y at point P(1,0) in the direction from pointP(1,0) to pointQ(2, – 1).Q3) Find the derivatives of the following functions a) If y=cos u, u=2x+/2 find dy/dx at point(0,2) b) Find for the function y =+ v c) if x? + cos-xy + In(y) + 2* =1 then find y' dr6. Find the directional derivative of the function f (x, y) = x² + x sin (y) at the point (1,7) in the direction of v= -27+ 3.
- Find the derivative of the function at Po in the direction of A. f(x.y,z) = xy + yz + zx, (1,- 1, - 2). A = 2i + 3j - 6k (DAf) (1. - 1. - 2) = (Simplify your answer.)A function z = (x, y) and a point P are given. Find the directional derivative of f in the indicated directions. f(x, y) = P = (1, 1) x²+y?+1' (a) In the direction of v = (1, - 1) (b) In the direction toward the point Q=(-2,-2)5. Consider the function f(x, y) = sin(r² + y²). Find the derivative of f(r, y) at the point P(-/2,0, sin(2)) in the (a) direction of (4,3). Sketch the level curve that goes through the point P(-V2, 0, sin(2)). (b) On the same graph, include the gradient at point P. (c) point P (-V2,0, sin(2)). Find the direction in which the function f(r,y) has no change at the (d) What is the fastest rate of change possible at the pointP (-V2,0, sin(2))? (e) Find the equation of the line normal to the surface at the point P(-V2,0, sin(2)).
- (c) The equation of a curve is given by, x²y² + 4y = x (i) Show that dy_1– 2xy? 4 + 2x²y dx Find the gradient of the curve at (0,0). (iii) Hence, find the equation of the tangent to the curve at (0,0).Find the directional derivative of f(x, y) = /4x + 3y at the point (2, 6) in the direction 57 radians. 34. Find the gradient Vf for the function f(x,y)= e* sin(7y) and the directional derivative at the point P (0,-) in the direction towards the point Q (3,-).
- Suppose that f (x, y) = 4e%* sin y. Find the directional derivative of f(x, y) in the direction of - 1, -4) and at the point (z, y) =(4, Find exact values. No decimalsQ10) use the Chain Rule to find the derivative of w- xy With respect to t along the path x-cost, y-sint.what is the derivatives value at t =Find the derivative of y with respect to x if y = (10x- 20x +20) ex. %3D dy dx (1,1) e Fntor voupncwor in the 2ncwor bay Show 4 (3x + 4) = 3 %3D - 3(3x + 4)² . 3 stmplify