Q.IB) If w=f(u, v) where u = tan ¹2 &v=ln(x² + y²), the show that: Əw dw aw +y ax dy 2- ду x-

Q: du ap B) Prove that dx n- dx v2 where u = f(x) and v = f(x).

A: To find  d(u/v) /dx

Q: {G) = -2x+5 firid f(2)

A: To find: The value of f1. Given: The function is fx=-2x+54. Calculation: Substitute x=1 in…

Q: Suppose Cov(X,Y) = 281. What is Cov(0.76X, 0.43Y)?

A: The objective of the question is to find the covariance of the two variables 0.76X and 0.43Y given…

Q: + 5)3; 3. dy

A:

Q: 3. Find y': y = 5sin3x

A: The given function is, y=5sin3x We need to find the derivative of the given function. The derivative…

Q: dæ . (x – 3)væ² – 6x + 5 Evaluate 2.

A: To evaluate the following integral

Q: (u x v) · v=,

A: The cross product of the vectors u and v is u×v which is a vector perpendicular to both the vectors…

Q: PIND F'): b. FG)- 4- ax*)

A: Given: f(x) = 4-3x25 To find: f'(x)

Q: 20. Let (). ()- u = v = If æu + yv = w. (æ, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2 (D) –1/2…

A: To find the value of x-y from the given vectors.

Q: d 3) Find 6 '+2t – 9)

A: To find:

Q: dx tan x -1 '+ 4dx de x- Vx

A: Taking #5 and #6 As per authoring guidelines, if the question number is not specified, the first…

Q: Evaluate 12 ST[-6zdy dz dx

A:

Q: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: (2y) dy. CSC

A: We will start with the substitution, csc-1(2y) = x and apply the integration by parts. And, will use…

Q: dy 3) Using the function y=f(x)=x², state which of the following uses of the notation: dx d and are…

A:

Q: Find y": Vy - Vx = Va

A:

Q: For the function y = x² + 2x, the value of dy when *=3 and dx=0.1 js -0.15 A) 0.15 B) C) - 0.8 0.8…

A: We will find out the required value.

Q: dx find . diven that x>0, using the substitution u =

A:

Q: ôw ôw + = 0 for w = Ax, y), x = u – v, and y = v – u and demonstrate the ди ду 6. Show that result…

A:

Q: dy (1 + æ)* Find for y dx Ans=

A:

Q: sinh x 20. 1x1-3 A) 2. B)-2. D) 0.

A:

Q: zyz-zy a) dx

A:

Q: dr. +37-10z

A: We have to evaluate the given integral.

Q: Find ∂z/∂t if z = sin(5x3-3y2), x = 2s2+t2, y = 2st3. Write in terms of the two independent…

A:

Q: [x³J2]=x³J2 dx ulgn O ihs O

A: Solution: Since J2=∑s=0∞-1s2+s!s!x22+2s Then, x3J2=∑s=0∞-1s2+s!s!·x3x22+2s…

Q: Determine the derivative of y = 24*. A. 24x+2 In 2 C. 34x+2 In 2 B. 63r+2 In 2 D. 44*+2 In 2

A: So in this we have to do simple derivative of given so I'm providing hand written solution for this

Q: a) Evaluate ſ Fa 1 dx. Vx(1+vx)*

A: Let,

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2