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Calculate $ \frac{\mathrm d}{\mathrm dt} f (g(t^2),g(t^4)), $ where $f$ is a differentiable function of two variables and $g$ is a differentiable function of one variable. Your answer should be expressed in terms of $f, g$ and their derivatives and/or partial derivatives.

I am assuming it is a partial derivatives question. I have never encountered one like this before. Any help would be much appreciated.

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    This is more like an `apply chain rule` question. The partial derivatives part in the question is because $\frac{df(x,y)}{dt}=\frac{\partial f}{\partial t}+\frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\frac{dy}{dt}$ (see [Wikipedia](http://en.wikipedia.org/wiki/Total_derivative)) -- I hope I didn't miss any $\partial$ while typing all this2012-11-27

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You presumably have a function $f(x,y)$, and somebody has set $x=g(t^2), y=g(t^4).$ Assuming $f$ doesn't depend on $t$ explicitly, $\frac{\mathrm d}{\mathrm dt} f (x,y)=\frac{\partial f}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial t}$. Now insert the given values for $x,y$ and use the chain rule.