Tagged Questions

Questions on the evaluation of derivatives or problems involving derivatives (for example, use of the mean value theorem).

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Pork roast defrost using calculus

I am really stuck on this problem for calculus and I could use some help A pork roast is removed from the freezer and left on the counter to defrost. The temperature of the pork roast was $−4^\circ C$...
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differentials in physics [migrated]

Often I find the following expressions in physics books: Say we have a current density $\vec{j}=\rho\vec{v}$ through a surface $\vec{F}$ of particles $N$ in the volume $V$ with the density $\rho=dN/dV$...
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Derivative of $x^y=y^x$ defines: $y=y(x)$ [closed]

I need to find the derivative. given that: $$x^y=y^x$$ defines: $$y=y(x)$$ Thank you!
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How to extend a function to be periodic and smooth?

Assume we have a function f(x) that is twice differentable on [0, L]. Let us define F(x) = f(x) on [0, L], F(x) = -f(-x) on [-L, 0], and F(x + 2L) = F(x) outside of [-L, L]. Thus, F(x) is ...
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Derivative of $y-2\sin(y)=x$ defines: $y=y(x)$

I need to find the derivative of $y'$ and $y''$ given that: $$y-2\sin(y)=x$$ defines: $$y=y(x)$$ Thank you!
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Derivatives of $f(x,t)=\varphi (x-at)+\psi (x+at)$

Given that $$f(x,t)=\varphi (x-at)+\psi (x+at)$$ $$u=x-at$$ $$v=x+at$$ We need to prove that: $$\frac{\partial^2 f}{\partial t^2}=a^2\frac{\partial^2 f}{\partial x^2}$$ We know how to calculate the ...