- #1

Adyssa

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## Homework Statement

I have a function z, and I need to find the derivative dz/dt "using the chain rule without substitution"

## Homework Equations

[tex]z = x^{2}y^{3} + e^{y}\cos x[/tex]

[tex]x = \log(t^{2})[/tex]

[tex]y = \sin(4t)[/tex]

## The Attempt at a Solution

[tex]\frac{\mathrm{d} z}{\mathrm{d} t} = 2xy^{3}+3x^{2}y^{2}+e^{y}\cos x-e^{y}\sin x[/tex]

[tex]\frac{\mathrm{d} z}{\mathrm{d} t} = 2\log(t^{2})\sin(4t)^{3}+3(\log(t^{2}))^{2}(\sin(4t))^{2}+e^{\sin(4t)}(\cos (\log(t^{2}))-\sin (\log(t^{2})))[/tex]

[tex]\frac{\mathrm{d} z}{\mathrm{d} t} = 4\log(t)\sin(4t)^{3}+3(2\log(t))^{2}(sin(4t))^{2}+e^{sin(4t)}(\cos (2\log(t))-sin (2\log(t)))[/tex]

I'm a bit stuck at this point, I feel like I should be able to do something with the log^2 and the e^sin . (cos(log) - sin(log))?

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