Problem of the Week

Updated at Jun 5, 2017 11:34 AM

To get more practice in calculus, we brought you this problem of the week:

How would you differentiate \(6x\sec{x}\)?

Check out the solution below!



\[\frac{d}{dx} 6x\sec{x}\]

1
Use Constant Factor Rule: \(\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))\).
\[6(\frac{d}{dx} x\sec{x})\]

2
Use Product Rule to find the derivative of \(x\sec{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[6((\frac{d}{dx} x)\sec{x}+x(\frac{d}{dx} \sec{x}))\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[6(\sec{x}+x(\frac{d}{dx} \sec{x}))\]

4
Use Trigonometric Differentiation: the derivative of \(\sec{x}\) is \(\sec{x}\tan{x}\).
\[6(\sec{x}+x\sec{x}\tan{x})\]

Done
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