Let $f(x) = \sqrt{3x+5}$. Obtain and prove a formula for the nth derivative. I'm having trouble finding the formula for the nth derivative.
I've computed the first three derivatives but not really sure what to do after that.
2026-04-07 20:01:38.1775592098
nth derivative of a radical function
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at first the first thee derivatives $$f(x)=(3x+5)^{1/2}$$ $$f'(x)=\frac{3}{2}(3x+5)^{1/2}$$ $$f''(x)=-\frac{9}{4}(3x+5)^{-3/2}$$ $$f'''(x)=\frac{81}{8}(3x+5)^{-5/2}$$ and can you proceed?