Problem of the Week

Updated at Mar 19, 2018 5:22 PM

How would you differentiate sec⁡xex\sec{x}{e}^{x}?

Below is the solution.



ddxsec⁡xex\frac{d}{dx} \sec{x}{e}^{x}

1
Use Product Rule to find the derivative of sec⁡xex\sec{x}{e}^{x}. The product rule states that (fg)′=f′g+fg′(fg)'=f'g+fg'.
(ddxsec⁡x)ex+sec⁡x(ddxex)(\frac{d}{dx} \sec{x}){e}^{x}+\sec{x}(\frac{d}{dx} {e}^{x})

2
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
sec⁡xtan⁡xex+sec⁡x(ddxex)\sec{x}\tan{x}{e}^{x}+\sec{x}(\frac{d}{dx} {e}^{x})

3
The derivative of ex{e}^{x} is ex{e}^{x}.
sec⁡xtan⁡xex+sec⁡xex\sec{x}\tan{x}{e}^{x}+\sec{x}{e}^{x}

Done
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