Problem of the Week

Updated at Sep 16, 2024 3:27 PM

How can we find the derivative of cos⁡z+3z\cos{z}+3z?

Below is the solution.



ddzcos⁡z+3z\frac{d}{dz} \cos{z}+3z

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)).
(ddzcos⁡z)+(ddz3z)(\frac{d}{dz} \cos{z})+(\frac{d}{dz} 3z)

2
Use Trigonometric Differentiation: the derivative of cos⁡x\cos{x} is −sin⁡x-\sin{x}.
−sin⁡z+(ddz3z)-\sin{z}+(\frac{d}{dz} 3z)

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
3−sin⁡z3-\sin{z}

Done
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