Calculus Formulas (Unit 3) Flashcards
Constant Rule
If c is a constant, F(x) = c, then F’(x) = 0
Product Rule
If h(x) = f(x) * g(x), then h’(x) = f’(x) * g(x) + g’(x) * f(x)
Quotient Rule
If h(x) = f(x) / g(x), then h’(x) = (f’(x) * g(x) - g’(x) * f(x)) / (g(x)^2)
Chain Rule
If h(x) = f(g(x)), then h’(x) = f’(u) * u’
Simple Power Rule
If f(x) = x^n, then f’(x) = n * x^n-1
Sum or Difference Rule
If h(x) = f(x) + g(x), then h’(x) = f’(x) + g’(x)
Derivative of sinx
cosx
Derivative of cosx
-sinx
Derivative of tanx
sec^2 (x)
Derivative of cotx
-csc^2 (x)
Derivative of secx
secx * tanx
Derivative of cscx
-cscx * cotx
Derivative of e^x
e^x
Derivative of lnx
1/x
Derivative of Log Base c (x)
1/(lna)x
log(A*B) =
log(A) + log(B)
log(A/B) =
log(A) - log(B)
log(A^n)
n * log(A)
log base c (c) =
1
log base x (1) =
0
sinx =
1/(cscx)
cosx =
1/(secx)
tanx =
1/(cotx)
secx =
1/(cosx)
cscx =
1/(sinx)
cotx =
1/tanx)
lim sinx/x = ?
x–>0
1
lim (1 - cosx)/x = ?
x –> 0
0
lim (1 + x)^(1/x) = ?
x –> 0
e
