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Derivatives formulas

Derivatives

QuestionAnswer
with c a constant, (c)’ 0
(x^n)’ n x^(n-1)
(e^x)’ e^x
(u+v)’ u’+v’
(u-v)’ u’-v’
Product Rule (uv)’ u’v+uv’
Quotient Rule (u/v)’ (u’v-uv’)/(v^2)
[sin(x)]’ cos(x)
[cos(x)]’ -sin(x)
[tan(x)]’ [sec(x)]^2
[sec(x)]’ sec(x)tan(x)
[csc(x)]’ -csc(x)cot(x)
[cot(x)]’ -[csc(x)]^2
Chain Rule [g(u(x))]’ g’(u(x)) u’(x)
with b>0, (b^x)’ (b^x)(ln(b))
[ln(x)]’ 1/x
with b>0, [log_b(x)]’ 1/(x ln(b))
Limit definition f’(x)= f’(x)=lim_(h->0) [f(x+h)-f(x)]/h
with c a constant, (cf)’ c f’
Created by: AntoineHerlin
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