Calculus Problems

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  1. Show that the derivative of \(\tan{x}\) is equal to \(\sec^2{x}\)

  2. Use the quotient rule to find the derivative of \(\sec{x}\)

  3. Use the quotient rule to find the derivative of \(\csc{x}\)

  4. What is the derivative of \(y = x{}\cos{(x)} \)

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

  6. Find the derivative of \(y = \frac{\tan{(2x)}}{x^2} \)

  7. Use the definition of \(e\) as the unique positive number for which \(\lim_{h \rightarrow 0}\frac{e^{h} - 1}{h} = 1\) and the definition of the derivative to show that derivative of the exponential function, \(f(x) = e^x\) is equal to \(e^x\)

  8. Determine the derivative of \(f(x) = 2x^5 - 3e^{6x}\)

  9. Find the derivative of \(y = {(2x - 5)}^2\)

  10. Find the derivative of \(f(x) = x^{3}e^{-2x}\)

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