1. Given z = e tan(x) + (2x + 3y)5 x = 7t² y = 5t +9 (a) Draw a tree diagram showing which variables depend on which. The variable z should be at the top. (b) Calculate the partial derivatives of z. dz dx (c) Calculate the derivatives of x(t) and y(t). dx dt dy dt || || дz ду

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Given
z = e' tan(x) + (2x + 3y)5
x=71²
y = 5t +9
(a) Draw a tree diagram showing which variables depend on which. The variable z should be at the top.
(b) Calculate the partial derivatives of z.
Əz
dx
(c) Calculate the derivatives of x(t) and y(t).
dx
dt
dy
dt
dz
dt
=
(d) Use the multivariable chain rule to calculate
||
dz
dt
||
z(t) =
əz
ду
(e) Now plug in for x and y in terms of t to find z as a function of t, then differentiate that function.
=
Transcribed Image Text:1. Given z = e' tan(x) + (2x + 3y)5 x=71² y = 5t +9 (a) Draw a tree diagram showing which variables depend on which. The variable z should be at the top. (b) Calculate the partial derivatives of z. Əz dx (c) Calculate the derivatives of x(t) and y(t). dx dt dy dt dz dt = (d) Use the multivariable chain rule to calculate || dz dt || z(t) = əz ду (e) Now plug in for x and y in terms of t to find z as a function of t, then differentiate that function. =
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