Find the directional derivative of f at P in the direction of a. f (x, y, z) = xy + z²; P(3,4,–4); a =i+j+k NOTE: Enter the exact answer. Duf :

Q: Find fa, fy, fyx and fy if f(x, y) = x + y + xy ух

A: This is second partial derivative so do the derivative like normal considering all other variable…

Q: The figure shows f, f', and f". Determine which is which. 2 y 0 -2 1

A: In this question we have to determine which is f, f' and f''.

Q: Find tan a. V[ ? (V5, -/7)

A:

Q: alla Find xy² R2² -dA, R= [0, 4] × [ - 2,2] x² +1

A:

Q: Assume that y varies jointly with x and the square root of z. f  y=30 when x=3 and z=25, then find…

A: Given y varies jointly with x & square revt at Z .If y = 30 when x = 3 & z = 25 .We have…

Q: d.r. , (- 1) 1,

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Q: Differentiate. y = (r2 – 4r)e" %3D

A: Given,            y = r2 - 4r er

Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: əz If z = f (x, y), find and for the following equation z=-2xy

A:

Q: 3) Find the function of y = 1) Reflect about the (2) Shift up (3) Shift X-axis 8 Units left 7units

A: The given function is y=x1) Reflect about x-axis2) shift up 8 units3) shift left 7 units

Q: 2y = 18 Enter your answer

A: Make the coefficient of y as 1 so do the calculation accordingly.

Q: Let v= (-4, -4, -3) Calculate: vxi= ( vx j= ( vxk= " "

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Q: Use a formula to express w as a function of t if  w =    4s + 9 and s = et − 1.  w =

A: We have given that,  w = 4s + 9 and  s = et − 1 Then,  We will find w in terms of t?

Q: Find all values of x so that v · v = 1, where

A: Given vector, v=12-12x That is v=12i-12j+xk

Q: ind V. (V × F), if F(x, y, z) = = V. (V X F) = ezi+ 6xe¹j - 3ek.

A: Topic:- vector algebra

Q: Find csc 0. (-5, V11) [?]/[] r

A: