| $y=k$ |
$y′=0$ |
$y = 5 \\y' = 0$ |
| $y = \sqrt{x}$ |
$y' = \frac{1}{2\sqrt{x}}$ |
$y = \sqrt{x} \\y' = \frac{1}{2\sqrt{x}}$ |
| $y = \log_a x$ |
$y' = \frac{1}{x \ln a}$ |
$y = \log_2 x \\y' = \frac{1}{x \ln 2}$ |
| $y = \cos x$ |
$y' = -\sin x$ |
$y = \cos x \\y' = -\sin x$ |
| $y = a^x$ |
$y' = a^x \ln a$ |
$y = 2^x \\y' = 2^x \ln 2$ |
| $y = \ln x$ |
$y' = \frac{1}{x}$ |
$y = \ln x \\y' = \frac{1}{x}$ |
| $y = x^n$ |
$y' = n x^{n-1}$ |
$y = x^3 \\y' = 3x^2$ |
| $y = e^x$ |
$y' = e^x$ |
$y = e^x \\y' = e^x$ |
| $y = \sin x$ |
$y' = \cos x$ |
$y = \sin x \\y' = \cos x$ |
| $y=k⋅F(x)$ |
$y' = k \cdot F'(x)$ |
$y = 3x^2 \\y' = 3(2x) = 6x$ |
| $y = F(x) + g(x)$ |
$y' = F'(x) + g'(x)$ |
$y = x^2 + \sin x \\y' = 2x + \cos x$ |
| $y=F(x)⋅g(x)$ |
$y′=F′(x)⋅g(x)+g′(x)⋅F(x)$ |
$y=x2⋅sinx \\ |
| y′= (2x⋅sinx)+(cosx⋅x2) = 2x \sin x + x^2 \cos x$ |
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| $y = \frac{1}{F(x)}$ |
$y′=-\frac{F'(x)}{F(x)^2}$ |
$y=\frac {1}{x^3+11} \\y' = -\frac{3x^2}{(x^3 + 1)^2}$ |
| $y = \frac{F(x)}{g(x)}$ |
$y′=\frac{F'(x)⋅g(x)-g'(x)⋅F(x)}{g(x)^2}$ |
$y=\frac{x^2+1}{x+2}\\ |
| y′=\frac{(2x⋅(x+2))−(1⋅(x^2+1))}{(x+2)^2}=\frac{2x(x+2)−(x^2+1)}{(x+2)^2} = \frac{2x^2+4x−x^2−1}{(x+2)^2} = \frac{2x^2 + 4x - x^2 - 1}{(x+2)^2} = \frac{x^2 + 4x - 1}{(x+2)^2}$ |
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| $y = D [f(g(x))]$ |
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| $y′ = f'(g(x)) \cdot g'(x)$ |
$y = ln(x^2+2) |
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| y' = \left( \frac{1}{x^2 + 2} \right) \cdot (2x)$ |
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