MTH 125 Calculus I Web Assisted Course

This material is based upon work supported by the
National Science Foundation
under Grant No. DUE-0336493

STEP- Science, Technology, Engineering, and Mathematics Talent Expansion Program

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Differentiation Formulas

	d/dx c = 0, c constant
	d/dx cf(x) = cf'(x), c constant
	d/dx [f(x) ± g(x)] = f'(x) ± g'(x)
	d/dx [f(x) * g(x)] = f(x) * g'(x) + g(x) * f'(x) (product rule)
	d/dx [f(x) / g(x)] = (g(x)f'(x) - f(x)g'(x))/([g(x)]²) (quotient rule)
	d/dx f[g(x)] = f'[g(x)] * g'(x) OR for u = g(x), d/dx f(u) = f'(u) * u' = f'(u) * g'(x) OR dy/dx = dy/du * du/dx (these are all chain rule)

GENERAL	SPECIFIC
d/dx uⁿ = nu^n-1 * u' d/dx lnu = u'/u d/dx e^u = e^u * u' d/dx sinu = cosu * u' d/dx cosu = -sinu * u' d/dx tanu = sec²u * u' d/dx arcsinu = u'/(SQRT(1 - u²)) d/dx arctanu = u'/(1 + u²) d/dx cotu = -csc²u * u' d/dx secu = secu tanu * u' d/dx cscu = -cscu cotu * u' d/dx a^u * u' ln a d/dx log_au = u'/(u ln a)	d/dx xⁿ = nx^{n - 1} d/dx lnx = 1/x d/dx e^x = e^x d/dx sinx = cosx d/dx cosx = -sinx d/dx tanx = sec² d/dx arcsinx = 1/(SQRT(1 - x²)) d/dx arctanx = 1/(1 + x²) d/dx cotx = -csc²x d/dx secx = secx tanx d/dx cscx = -cscx cotx d/dx a^x = a^x ln a d/dx log_ax = 1/(x ln a)


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