Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(6) = −4, g'(6) = −8, h(6) = 9, h'(6) = 5, fr(-4,9): -9, and fy(-4, 9) = 8, find dz/dt when t = 6. W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. If u(2, -6)=-5, us(2, −6) = −2, u(2, −6) = −7, v(2, −6) = −9, vs(2, −6) = 3, v(2, -6)=7, F(-5, -9) = 8, and F(-5, -9) = 4, then find the following: W (2,-6)= W₁(2, -6)=

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t).
If g(6) = −4, g'(6) = −8, h(6) = 9, h'(6) = 5, fr(-4,9): -9, and fy(-4, 9) = 8, find dz/dt
when t = 6.
Transcribed Image Text:Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(6) = −4, g'(6) = −8, h(6) = 9, h'(6) = 5, fr(-4,9): -9, and fy(-4, 9) = 8, find dz/dt when t = 6.
W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable.
If u(2, -6)=-5, us(2, −6) = −2, u(2, −6) = −7, v(2, −6) = −9, vs(2, −6) = 3,
v(2, -6)=7, F(-5, -9) = 8, and F(-5, -9) = 4, then find the following:
W (2,-6)=
W₁(2, -6)=
Transcribed Image Text:W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. If u(2, -6)=-5, us(2, −6) = −2, u(2, −6) = −7, v(2, −6) = −9, vs(2, −6) = 3, v(2, -6)=7, F(-5, -9) = 8, and F(-5, -9) = 4, then find the following: W (2,-6)= W₁(2, -6)=
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