Solving Differential Equations

mattmannmf
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Solve the following:

d/dt cos(theta)
d/dt t sin(theta)
d/dt r cos (theta)
d/dt r^2 (theta)
d/dt e^ (-3x)
d/dt (x^2 + y^2)

I would assume all by the second one are 0 since your solving for terms dt and not theta, x, y, or r... I don't think its right at all. I know it goes something like this:
d/dt f(x) = dy/dx * dx/dt
I just am not sure how to grasp what I'm doing wrong.
 
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Is theta a function of t?
 
what do you mean?
 
is \theta =\theta (t), otherwise the derivative will be non-zero.
 
all it says its differential calculus and gives the problem as I stated above
 
From the title of the thread ("Calculus Chain Rule"), I think it's reasonable to assume that \theta is a differentiable function of t, and that you are meant to use the chain rule.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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