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Show that $f^2 - g^2 = C$

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#calculus #derivatives
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What is the derivative of $xf(x)$?

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#calculus #derivatives
163
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Suppose the function $\sqrt{x}$ is continuous at any $c>0$. Show that this function is differentiable at any $c>0$ and find $f'(c)$.

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#derivatives #continuity
121
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Prove that this function is NOT differentiable at $c=0$.

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#derivatives #proof-verification #continuity
37
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How to calculate tangent of function, which has to cross certain value on x axis

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#calculus #functions #derivatives #tangent-line
2.4k
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derivative of square of dot product

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#derivatives #vectors
481
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derivative of a function of vector norm with respect to vector

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#calculus #derivatives #vectors #normed-spaces
3.6k
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proof of Taylor's theorem

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#real-analysis #derivatives
52
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Functions where critical numbers equal points of inflection

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#ordinary-differential-equations #functions #derivatives
1k
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What is the closest point to $(0,-1/2)$ on the curve $x^2+2y=0$? Why can't I differentiate over $y$?

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#calculus #derivatives #optimization
143
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Proof verification: derivative of $x^n$

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#calculus #derivatives #proof-verification
1.4k
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Finding a bounded function with unbounded derivative at zero

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#functions #derivatives #examples-counterexamples
650
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Show that $f^{(k)}(x_0)=0$ for all $k=0,1,2,...,n$ if and only if $g(x)= {f(x)}/{(x-x_0)^{n+1}}$ is continuous at $x_0$.

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#real-analysis #derivatives
234
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Does the argmax of $x^{1/x} = e$, and why?

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#derivatives #maxima-minima
347
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$\lim\limits_{h\to0}\frac{f(x-h)-f(x)}{h}=-f'(x)$ if $f'(x)$ exist

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#real-analysis #derivatives

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