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QUESTION 7 Using implicit differentiation to find az ax for x2 + xy -sin(z)-0 y + COSZ-X Х COSZ-X y COS2-X y +Z sinz-X
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7. Find fryzx, for f(x, y, z) = 3 + 2?x – xyz + x+y 8. Use the chain rule to calculate that t = 0, if z = sin(xy), x = 1+1, y = 12 + 2t. 9. Use the chain rule to find us at (u, v) = (1,0), when z = xy, x = u +v?, y = x + v.
- bram , July It, 2014 I (a) If z=f(x,y) welt u=x²-yz and U=xy find the Tacoblan of le, U with respect to yy. (b) Use the chain rule to evaluate az and dz When Z= sin ax cosby for x=sity-s-t व
Find dz d given: z = xeyy, x = = to, y= – 2 + 2t dz dt Your answer should only involve the variable t. Let z(x, y) = xºy where x = tº & y = +8. Calculate dz by first finding dt dx -& dt dy and using the chain rule. dt dx d = dy dt Now use the chain rule to calculate the following: dz dt
Use the Chain Rule to find dz/dt. z = sin(x) cos(y), x= VE, y = 7/t dz dt 11
The contour diagram in Figure 6(a) describes the hyperbolic paraboloid z = f(x, y) = I y. The bold lines represent the r and y axes. (a) (b) Figure 6 i) Through a change of variables u = r+y and v = r-y, show that f can be rewrit- ten in the standard form of a hyperbolic paraboloid. Such a transformation is shown in Figure 6(b) where the bold lines now represent the u and v axes. az ii) Use...
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the derivative of the function y - tan-(x-v1+x? ). Problem 5. Find the derivative of the function y = sin(2x+1). Problem 6. Find the derivative of the function h(x) = sinh(x?). Problem 7. Find the limits. Use L'Hospital's Rule where appropriate. I (a) lim x’e-* (b) lim (sin x In x) x0+
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = ". Find fu and , using the chain rule.
az (b) Compute at (0,0,0) if z is a function of x and y given implicitly by the equation дх 3 + z2 + ye2 + z cos y = 0
Differentiate implicitly to find the first partial derivatives of z. x In(y) + y2z + ? = 49 az Ox = az ay = 10. (-/1 Points] DETAILS ALC11 13.6.009. Find the directional derivative of the function at P in the direction of v. g(x, y) = x2 + y2, P(7, 24), v = 5i - 123