Calculus Problems

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  1. Find the derivative of \(y = e^{2x}(x-1) + 8 - 5x^2\)

  2. Find the first derivative of \(y = 2x \sin({x^2})\)

  3. Use the product rule to find the derivative of
    \(f(x) = (x^3 + 5x)(2x^2)\)

  4. Find the derivative of \(f(x) = \sin{x}(x^2 + 5)\)

  5. Use the quotient rule to find the derivative of \(y = \frac{5x}{6x^2 + 2x}\)

  6. Use the quotient rule to find the derivative of the following funciton,
    \(f(x) = \frac{x - 1}{x^2 + 2x + 1}\)

  7. Find \(f\prime(x)\)
    \(f(x) = \frac{5x^2 - 1}{2x^3 + 3}\)

  8. Given \(f(x)\), find the equation of the tangent line at the point \((-1, -2)\)
    \(f(x) = \frac{4x}{(1 + x^2)}\)

  9. Use the definition of the derivative to show that the derivative of \(\sin{x}\) is equal to \(\cos{x}\)

  10. Show that the derivative of \(\cos{x}\) is equal to \(-\sin{x}\)

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