Question

In: Math

(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx. (2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3),...

(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx.

(2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3), x2 = lnx3. find ∂f/∂x3, and df/dx3.

Solutions

Expert Solution


Related Solutions

Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of...
Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of F across S, the top part of the paraboloid x2 + y2 + z = 2 that lies above the plane z = 1 and is oriented upward. Note that S is not a closed surface.
solve for x: [x * sqrt(1+x2)] + ln[x + sqrt(1+x2)] = 25
solve for x: [x * sqrt(1+x2)] + ln[x + sqrt(1+x2)] = 25
Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 8)j + zk. Find the...
Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 8)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 28 that lies above the plane z = 3 and is oriented upward. S F · dS =
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the...
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 29 that lies above the plane z = 4 and is oriented upward.
1. The function f(x, y) = ln(x3 + 2) / (y2 + 3) (this function is...
1. The function f(x, y) = ln(x3 + 2) / (y2 + 3) (this function is of a fraction format) : a. has a stationary point at (1, 0) b. has a stationary point at (0, 0) c. has a stationary point at (0, 1) d. has no stationary points 2. Which of the following functions don’t have unit elasticity at P = 6? a. Demand: Qd = 24 - 2 P b. Demand: Qd = 10/P c. Demand: log...
Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if...
Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if 1<X1<2 -1<X2<0 -X2-1<X3<0                         0 otherwise Find Cov(X2, X3)
1. Differentiate the following functions A. y=ln(x+sqrt(x^2 -1)) B. y=ln(sinx) C. y=xlnx-x D. y=e^x(sinx)
1. Differentiate the following functions A. y=ln(x+sqrt(x^2 -1)) B. y=ln(sinx) C. y=xlnx-x D. y=e^x(sinx)
((sqrtx)+1)dy/dx=(ysqrtx)/(x) + sqrt(y/x), y(2)=1
((sqrtx)+1)dy/dx=(ysqrtx)/(x) + sqrt(y/x), y(2)=1
Suppose that a firm has the p production function f(x1; x2) = sqrt(x1) + x2^2. (a)...
Suppose that a firm has the p production function f(x1; x2) = sqrt(x1) + x2^2. (a) The marginal product of factor 1 (increases, decreases, stays constant) ------------ as the amount of factor 1 increases. The marginal product of factor 2 (increases, decreases, stays constant) ----------- as the amount of factor 2 increases. (b) This production function does not satisfy the definition of increasing returns to scale, constant returns to scale, or decreasing returns to scale. How can this be? (c)Find...
Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln...
Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln x +y/x)dx = (1-lnx)dy Solve (y^2+yx)dx - x^2dy =0 Solve (x^2+2y^2)dx = xydy Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2) Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2) Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2 Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0 Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1 6. Mixture Problem Initially 40 lb of salt is dissolved in a large...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT