find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r, s)=(1, -1)

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: 4. Compute the first fundamental form.

A: Given xu,v=u2-cosv,u+sint, cosv

Q: 3 z'= 2(x"+Z) Arrang e in linear form: dy Q) or dx

A:

Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

A:

Q: Q2) Find az/du and äz/au for the following function and then find dz/ou and az/dv at the given…

A:

Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

A:

Q: The differential of the function f(x,t)= e cos(2 tt) at the point (x,t)= (0,1) is given by -2dx +2…

A: Topic- Application of derivatives

Q: How did he get the value inside the circle f(x, y)=x² + sin(xy) Vf=x*+sin(xy)) i+ d(x²+sin(xy)), dx…

A: given ∇f(1,0)=2i+j we have to find the direction in which the directional derivative has some value.

Q: Find directional derivative for f(x,y) = y +, Xo = 4, yo = 5, nx = 1, ny = 0. df ðf af -Nx + -Ny=|…

A: We will evaluate the required values.

Q: A psychologist conducted a study to examine the nature of the relation, if any, between an…

A: Ans a. What is the estimated logistic regression line.

Q: Find the second derivative of the vector-valued function r(t) = (7t + 5 sin(t))i + (4t + 5 cos(t))j…

A:

Q: For which z values of the complex functions given below have the derivative (f'(z)), obtain a) f(z)…

A: The derivative of A function f at z=z0 is defined as  If f is polynomial in z , then f is…

Q: determine the relation x^2 + y^2 = 13. dy/dx in terms of x and y using implicit differentiation.

A:

Q: Find the equation of the least squares using matrix methods. Use your equation in a above to…

A:

Q: 5. Compute the lenght of the curve u = t, v=0 from t = 0 to t = 1 using the first fundamental form.

A: Suppose, a continuous function is provided over a certain interval. The arc length is the length…

Q: 2. (5) Find f, for the function f(x, y) = sin (x + y²)

A:

Q: = (u² - cos v, u + sint, cos v) x(u, v):

A:

Q: Find f'(z) when f(z) = J, 0, if z = 0 if z = 0

A: fz=z¯ 2zif z≠00if z=0 To Find: f'z

Q: for the functions below: a) if y-sinu, u-3x+n find dy/dx at point(0,1) b) Find for the function y =+…

A: we are given: y=sin u and u=3x+π ⇒y=sin (π+3x)=- sin 3x ⇒dydx=-3 cos 3xdydx(0,1)=-3 cos 3(0) =-3…