Try It Yourself#
Exercise 1#
Find all values of \(t\) such that
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Answer: \(t = 2\), \(t=-1/2\)
Exercise 2#
Find all values of \(x\) such that
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Answer: \(x = 3\), \(x=1\)
Exercise 3#
Expand and simplify
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Answer: \(-3x-\ln(x) - x\ln(5)\)
Exercise 4#
Compute the derivative of
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Answer: \(15t^2e^{5t^3+3}\)
Exercise 5#
Compute the derivative of
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Answer: \(15t^2/(5t^3+3)\)
Exercise 6#
Compute the derivative of
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Answer: \(\frac{3}{x} - \frac{2}{2x-1}\)
Exercise 7#
Given the supply equation \(s(x)\) for video accelerator boards to be
determine the marginal revenue function, \(R'(x)\).
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Answer: \(x(1+2\ln(x))\)
Exercise 8#
Find the equation of the tangent line to the curve
at the point \((1,0)\).
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Answer: \(y=2(x-1)\)
Exercise 9#
Let
Find \(\displaystyle \frac{dy}{dx}\).
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Answer: \(y' = (6x^5 - ye^{xy})/(xe^{xy}-5y^4)\)
Exercise 10#
Let
Find \(\displaystyle \frac{dy}{dx}\) at the point \((1,1)\).
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Answer: \(y' = -3/2\)
Exercise 11#
Use logarithmic differentiation to compute the derivative of
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Answer: \(\frac{x^5 (x^3+4x)^7}{\sqrt{6x+2}}\left[\frac{5}{x} + \frac{7(3x^2 + 4)}{x^3+4x} - \frac{3}{6x+2}\right]\)
Exercise 12#
Compute the derivative of
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Answer: \((x^2 + 3)^{7x+1}\left[7\ln(x^2+3) + \frac{2x(7x+1)}{x^2+3}\right]\)