# Dammit.  More calculus questions!

**URL:** <https://boards.straightdope.com/t/dammit-more-calculus-questions/151772>\
**Category:** Factual Questions\
**Created:** [January 31, 2003, 1:21am UTC](https://boards.straightdope.com/t/dammit-more-calculus-questions/151772 "2003-01-31T01:21:43Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\
**Post date:** [January 31, 2003, 1:21am UTC](https://boards.straightdope.com/t/dammit-more-calculus-questions/151772/1 "2003-01-31T01:21:43Z")

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Ooookay. It never ends, I tell you.

1. The derivative of Kx^n is of course nkx^(n-1.) But what is the derivative of k^x? For instance, f I have 5^x, is it x5^(x-1)?

2. The derivative of sin(x) is, I assume, cos(x.) What’s the derivate of, say 4000sin(x)?

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**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\
**Post date:** [January 31, 2003, 1:28am UTC](https://boards.straightdope.com/t/dammit-more-calculus-questions/151772/2 "2003-01-31T01:28:42Z")

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D(a[sup]x[/sup]) = a[sup]x[/sup] ln a

D(k sin(k)) = k cos(x)

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**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\
**Post date:** [January 31, 2003, 1:33am UTC](https://boards.straightdope.com/t/dammit-more-calculus-questions/151772/3 "2003-01-31T01:33:33Z")

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a[sup]x[/sup] = e[sup]xln(a)[/sup]. That’s where the first one comes from.

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**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\
**Post date:** [January 31, 2003, 1:43am UTC](https://boards.straightdope.com/t/dammit-more-calculus-questions/151772/4 "2003-01-31T01:43:18Z")

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Oops. D(k sin( **x** )) = k cos(x)