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- Find the gradient of the function z = ln(x2 − y) /(x − 4), at the given point (2, 3)Differentiate the function. y = (2x* -x+ 1) (-x° + 3) - x+ y' =OFind the derivative of the function at P, in the direction of A 1) f(x, y) = 2xy- 3y', P.(5,5), A = 4i + 3j g(x, y) = x-(y/x)+ 3 sec (2xy), P(1,1), A = 12i+5j Ans. 31/13 Ans. -4 3) f(x, y, z) = xy+ yz + xz, P,(1,-1,2), A= 3i+ 6j- 2k Ans. 3 4) g(x, y, z) = 3e" cos(yz), P(0,0,0), A= 2i +j-2k Ans. 2
- How do I compute a value within 0.01 using linear approximation when it is a cosine function?(c) The equation of a curve is given by, x²y² + 4y = x (i) Show that dy_1- 2xy2 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 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.)
- given that x^2y^2+3x=y^3-1 use implicit differeniation to find the value of y'(1,2) a.3/2 b.13/8 c.11/8 d.5/4What is the derivative of f(x, y, =)=x'y+y: at P(5,1,0) in the direction of P(5,1,0) through to Q(2. -3,12) line. O a. -118/13 O b. 124/17 O C. -112/15 O d. -142/13 O e. 137/15The directional derivative of o = 5x2y – 5y2z + 2.5z2x at the point P(1, 1, 1) in the direction of the line * X-1 2 y-3 = Z -2