Differentiate, but do not simplify ##f(x)=5^{tan(\sqrt{ x})}##

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ttpp1124
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Homework Statement
can someone see if my work is right?
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Handwritten chain-rule derivation of f(x) = 5^tan(√x), reducing dy/dx step by step to a boxed result: ln(5)/2 · 5^tan(√x) · sec²(√x) / √x.
 
If you continue in the STEM fields, you will find yourself with a job where you are responsible for doing correct calculations on your own. Out in the real world people don't check your work because either they don't know how (you're the expert), or they have their own work to do. The ultimate check is the bridge collapses (or not), or the patient dies (or not), or you have a really happy (or pissed off) customer.

An important skill to develop is the ability to check your own work. Step one is do the calculation, step two is convince yourself that you did it right (because we all make mistakes).
 
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