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10 questions from this quiz
vu′−uv′v2\frac{vu' - uv'}{v^2}v2vu′−uv′
The numerator
To account for how the denominator changes
Identify functions u(x)u(x)u(x) and v(x)v(x)v(x)
−4x(x2−1)2\frac{-4x}{(x^2 - 1)^2}(x2−1)2−4x
xcos(x)−sin(x)x2\frac{x\cos(x) - \sin(x)}{x^2}x2xcos(x)−sin(x)
When the functions are composite functions
3e3x3e^{3x}3e3x
dydx=−8c(4x−c)2≠0\frac{dy}{dx} = \frac{-8c}{(4x-c)^2} \neq 0dxdy=(4x−c)2−8c=0
2x−3x2e3x\frac{2x - 3x^2}{e^{3x}}e3x2x−3x2
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