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Magazine Problem 30
Compute the derivatives of the functions. For extra practice, and to check your answers, do some of these in more than one way if possible. \(\frac{(x-1)(x-2)}{x-3}\)
Problem 31
Compute the derivatives of the functions. For extra practice, and to check your answers, do some of these in more than one way if possible. \(\frac{2 x^{-1}-x^{-2}}{3 x^{-1}-4 x^{-2}}\)
Problem 32
Compute the derivatives of the functions. For extra practice, and to check your answers, do some of these in more than one way if possible. \(3\left(x^{2}+1\right)\left(2 x^{2}-1\right)(2 x+3)\)
Problem 33
Compute the derivatives of the functions. For extra practice, and to check your answers, do some of these in more than one way if possible. \(\frac{1}{(2 x+1)(x-3)}\)
Problem 34
Compute the derivatives of the functions. For extra practice, and to check your answers, do some of these in more than one way if possible. \(\left((2 x+1)^{-1}+3\right)^{-1}\)
Problem 35
Compute the derivatives of the functions. For extra practice, and to check your answers, do some of these in more than one way if possible. \((2 x+1)^{3}\left(x^{2}+1\right)^{2}\)
Problem 36
Find an equation for the tangent line to \(f(x)=(x-2)^{1 / 3} /\left(x^{3}+4 x-1\right)^{2}\) at \(x=1\).
Problem 37
Find an equation for the tangent line to \(y=9 x^{-2}\) at (3,1) .
Problem 38
Find an equation for the tangent line to \(\left(x^{2}-4 x+5\right) \sqrt{25-x^{2}}\) at (3,8).
Problem 39
Find an equation for the tangent line to \(\frac{\left(x^{2}+x+1\right)}{(1-x)}\) at (2,-7) .
