Problem of the Week

Updated at Oct 28, 2024 4:43 PM

This week we have another calculus problem:

How would you differentiate sec⁡u+eu\sec{u}+{e}^{u}?

Let's start!



ddusec⁡u+eu\frac{d}{du} \sec{u}+{e}^{u}

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddusec⁡u)+(ddueu)(\frac{d}{du} \sec{u})+(\frac{d}{du} {e}^{u})

2
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
sec⁡utan⁡u+(ddueu)\sec{u}\tan{u}+(\frac{d}{du} {e}^{u})

3
The derivative of ex{e}^{x} is ex{e}^{x}.
sec⁡utan⁡u+eu\sec{u}\tan{u}+{e}^{u}

Done
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