# Tagged Questions

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

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### Finding Solutions (with only pen and paper)

For what least value of $k$ does the equation:$$e^x=kx^2$$ Have 3 solutions? Let $f(x)=e^x$ and $g(x)=kx^2$. For a positive $k$, drawing a rough graph of $f(x)$ and $g(x)$ does show 2 solutions of ...
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### Does infinitely differentiable imply analytic? [duplicate]

I know that analytic implies infinitely differentiable, but is the converse always true as well?
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### Functions and Derivatives

Generaly curious: Let there be a set of functions: Will the sum of the derivatives of the functions be equal to the derivative of the sums?
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### Raising index on covariant derivative

So suppose $X$ is some vector field and $t$ is a tangent vector to some curve on some smooth manifold. Then $t^a\nabla_a X$ gives the directional derivative of the vector field in the direction of ...
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### Applications of $f(x_0)=f'(x_0)$

If a function $f(x)$ has a derivative $f'(x)$ then where $f'(x_0) = 0$ there is an extreme point at $x=x_0$. And where $f''(x_0)=0$ there is an inflection point at $x=x_0$. I am asking are there any ...
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### Radon-Nikodym derivative as a Martingale

Let $(\Omega,\mathscr{F}, P)$ be a probability space, let $\nu$ be a finite measure on $\mathscr{F}$, and let $\mathscr{F}_{1}$, $\mathscr{F}_{2}$,... be a non-decreasing sequence of $\sigma$-fields ...
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### Partial Derivative with product & chain rule

I cannot for the life of me work out the answer to this partial derivative. $$\frac{\delta}{\delta x}\left(\frac{x^2}{(x+y)^2(x+z)^2}\right)$$ My first thought was: Split into two equations: ...