derivatives & domain and range Flashcards
dy/dx (sinx)
cos(x)
dy/dx (cosx)
-sin(x)
dy/dx (tanx)
(sec^2)(x)
dy/dx (cscx)
-cot(x)csc(x)
dy/dx (secx)
tan(x)sec(x)
dy/dx (cotx)
-(csc^2)(x)
dy/dx (e^x)
e^x
dy/dx [a^x]
ln(a) * a^x
dy/dx [ln(x)]
1/x
dy/dx [log(base b)(x)]
[1/(ln(b))] * (1/x)
dy/dx (arcsin(x))
1/√(1-x^2)
dy/dx (arccos(x))
-1/√(1-x^2)
dy/dx (arctan(x))
1/(1+x^2)
dy/dx (arccsc(x))
-1/(abs(x)√(x^2 - 1)) , abs(x) > 1
dy/dx (arcsec(x))
1/(abs(x)√(x^2 - 1)) , abs(x) > 1
dy/dx (arccot(x))
-1/(1+x^2)
domain and range of cos(x)
domain: all real numbers
range: [-1,1]
domain and range of sin(x)
domain: all real numbers
range: [-1,1]
domain and range of tan(x)
domain: x ≠ (2n-1)(π/2)
range: all real numbers
domain and range of cot(x)
domain: x ≠ nπ
range: all real numbers
domain and range of csc(x)
domain: x ≠ nπ
range: (-∞ , -1] U [1, ∞)
domain and range of sec(x)
domain: x ≠ (2n-1)(π/2)
range: (-∞ , -1] U [1, ∞)
domain and range of arccos(x)
domain: [-1,1]
range: [0,π]
domain and range of arcsin(x)
domain: [-1,1]
range: [-π/2 , π/2]
domain and range of arctan(x)
domain: all real numbers
range: (-π/2 , π/2)
domain and range of arccsc(x)
domain: (-∞ , -1] U [1, ∞)
range: [-π/2 , π/2], y ≠ 0
domain and range of arccot(x)
domain: all real numbers
range: (0,π)
domain and range of arcsec(x)
domain: (-∞ , -1] U [1, ∞)
range: [-π/2 , π/2], y ≠ π/2
