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Differentiability in terms of alpha

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#real-analysis #derivatives
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Cross partial with implicit differentiation

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#derivatives #partial-derivative #implicit-differentiation #implicit-function-theorem
369
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What does second-order derivative really tell you geometrically?

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#calculus #derivatives
162
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Minimize the cost of material of a can

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#derivatives #optimization #maxima-minima #economics
77
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Let $f$ be differentiable on $(a,b)$. Prove that for $c$ not a supremum of $f'$ there is $x_1,x_2$ st. $f'(c)=\frac{f(x_1)-f(x_2)}{x_1-x_2}$.

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#derivatives #continuity
114
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How to find the mean value for $\frac{1}{x^2+1}$?

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#real-analysis #derivatives
67
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Prove that if $\lim_{x \to +\infty}f(x)= 1$ and $\lim_{x \to +\infty}f'(x) = c$ then $c=0$.

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#derivatives #continuity
103
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Calculus: Find $\lim\limits_{h \to 0}{\frac{f(x+h)-f(x)}{h}}$ for $f(x)=\cos(x^2)$

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#calculus #limits #derivatives
242
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Chain rule for equations of multiple variables

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#analysis #derivatives #partial-derivative #chain-rule
385
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On real roots of a polynomial equation

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#real-analysis #complex-analysis #ordinary-differential-equations #derivatives #polynomials
126
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How do you find the first order partial derivatives of a function that contains another derivable function?

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#calculus #multivariable-calculus #derivatives #partial-derivative
221
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Generalization of the chain rule using upper derivatives

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#real-analysis #derivatives
165
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Find the tangent line for the following: $(\operatorname{arcsec} x)^2$ at $x = 2$

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#calculus #derivatives #hyperbolic-functions #tangent-line
58
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$\vert f \vert$ is always differentiable at $x=0$

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#real-analysis #analysis #derivatives
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Finding the derivative of $\ln(\sin(x))$ using first principles.

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#calculus #limits #derivatives

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