# Calc 1 review

 ∫ cot(x) dx = = ln(|sin(x)|) + C ∫1/cos2(x) dx= = tan(x) +C d/dx [f(x)/g(x)]= =  [f'(x)g(x)-g'(x)f(x)]    ----------------------            (g(x))2 logarithmic rule logbMN= =logbM +logbN logarithmic rule logb(M/N)= =logbM-logbN logarithmic rule logbMp = =P(logbM) d/dx[sin-1 u]= =     1  ---------- (du/dx)   √(1-u2) d/dx [csc-1 u] = =      -1   ------------  (du/dx)   |u|√(u2-1) d/dx[cos(x)]= = -sin(x) d/dx[tan(x)]= = sec2(x) ∫1/x dx= = ∫x-1 dx = ln(|x|) + C ∫[f(x)+g(x)] dx = = ∫f(x) dx + ∫g(x) dx ∫[f(x) -g(x)] = =∫f(x) dx - ∫g(x) dx d/dx [sin(u)] = = cos(u) * du/dx d/dx [cos(u)]= = -sin(u) * du/dx d/dx [eu]= =eu * du/dx ∫ax dx = =(ax)/(ln(a)) +C ∫sec2(x) dx = =∫1/(cos2(x)) dx =tan(x) +C d/dx [c]= = 0 d/dx [csc(x)]= = -csc(x)cot(x) d/dx (x) = 1 d/dx (ex)= =ex d/dx (bx)= = bxln(b) d/dx[sin(x)]= =cos(x) d/dx [ln(x)]= =1/x x>0 d/dx [ln(u)]= =1/u * (du/dx) x>0 d/dx [cos(u)]= = -sin(u) * du/dx d/dx [eu]= = eu * du/dx ∫ax dx= =(ax)/ln(a) +C ∫sec2(x)dx= =∫1/cos2(x) dx =tan(x)+C d/dx [sec-1(u)]= =         1   --------------  * (du/dx)   |u|√(u2 +1) d/dx [tan-1(u)]= =     1   --------- * (du/dx)     u2 +1 d/dx [c f(x)]= =cf'(x) du/dx [u(x)]n= =n[u(x)]n-1 * u'(x) or =nun-1 *du/dx d/dx [csc(u)]= = -csc(u)cot(u) *du/dx d/dx [tan(u)]= =sec2(u) * du/dx d/dx [sec(u)]= =sec(u)tan(u) * du/dx ∫tan(x) dx = = ln|sec(x)| +C or = -ln|cos(x)|+C d/dx[sec(x)]= sec(x)tan(x) d/dx (xn)= =n(xn-1) d/dx[cot(x)]= = -csc2(x) ∫cot(x) dx= = ln|sin(x)| + C ∫sec(x) dx = = ln|sec(x)+tan(x)| + C d/dx[f(x)±g(x)]= = f'(x) ± g'(x) d/dx [f(g(x))]= = f'(g(x))*g'(x) d/dx [sec(x)]= = sec(x)tan(x) d/dx [cot(x)]= = -csc2(x) d/dx [logax]= = 1/(x*ln(a)) d/dx logau = = 1/u*ln(a) * du/dx ∫csc2(x) dx = = -cot(x)+C ∫1/(√1-x2) dx = =sin-1(x) +C ∫sec2(x) dx = = tan(x) +C ∫cot2(x) dx= = -cot(x) - x + C Authorsaucyocelot ID358563 Card SetCalc 1 review DescriptionReview: derivatives and integration Updated2023-10-06T14:08:55Z Show Answers