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Matrix differentiation involving exponential function

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#matrices #derivatives
34
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Parameterized derivative

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#derivatives
53
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$G'(0) = \int_{[0,1] \backslash Z(g)} h(x) \cdot \text{sign}(g(x)) \mathrm{d}x$

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#calculus #real-analysis #integration #sequences-and-series #derivatives
103
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Show example where $F(x) = \int_0^x f(t) \, dt$ but $F'(x_0) \neq f(x_0)$

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#real-analysis #integration #derivatives #definite-integrals
1000
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Remainder in Lagrange form of $\ln (1-x)$

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#calculus #real-analysis #derivatives #taylor-expansion
810
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Link between polynomial and derivative of polynomial

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#functions #derivatives #polynomials #roots #real-numbers
267
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Theoretical Solution for this Poisson Equation Problem

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#ordinary-differential-equations #derivatives #partial-differential-equations #boundary-value-problem #poissons-equation
85
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Slope of a Curve at a Point

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#calculus #derivatives
1.1k
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Notation for the derivative of a function: $f'$ or $f'(x)\;$?

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#calculus #derivatives #notation
131
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Slope, Tangent and Rate of Change

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#calculus #derivatives
286
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Prove or disprove that if $\lim\limits_{x\to0^+}f(x)=0$ and $|x^2f''(x)|\leq c$ then $\lim\limits_{x\to0^+}xf'(x)=0$

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#real-analysis #limits #derivatives
46
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$x=\frac{1}{4}(t+e^{-t})$, $y=e^{-\frac{t}{2}}$, prove that $yy''(x)=(y'(x))^2\cdot \sqrt{1+(y'(x))^2}$: what am I doing wrong?

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#calculus #derivatives
66
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If $F(x)=\frac{x^4-3}{x^4+1}$ is a primitive of $f(x)$ find $\int_{0}^{1} xf(x) dx$

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#calculus #real-analysis #integration #derivatives #definite-integrals
101
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Find the derivative of $y={1\over2}\tan^4x-{1\over2}\tan^2x-\ln\cos x$

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#calculus #derivatives #trigonometry #proof-verification
296
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Finding derivative of $f(x)$ where $f(xy) = f(x) + f(y)$ - without change of variable

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#limits #derivatives #logarithms #change-of-variable

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