Calculus Concepts
The Basics
d/dx sin(u) = cos(u) du/dx
Example:
d/dx sin(3x)
u = 3x, so du/dx = 3
Therefore the answer is cos(3x) * 3 or
3 cos(3x)
d/dx cos(u) = -sin(u) du/dx
Example:
d/dx cos(x^2)
u = x^2, so du/dx = 2x
Therefore the answer is -sin(x^2) * 2x or
-2x sin(x^2)
d/dx tan(u) = sec^2(u) du/dx
Example:
d/dx tan(5x)
u = 5x, so du/dx = 5
Therefore the answer is sec^2(5x) * 5 or
5 sec^2(5x)
d/dx cot(u) = -csc^2(u) du/dx
Example:
d/dx cot(3x^3)
u = 3x^3, so du/dx = 9x^2
Therefore the answer is -csc^2(3x^3) * 9x^2 or
-9x^2 csc^2(3x^3)
d/dx sec(u) = sec(u)tan(u) du/dx
Example:
d/dx sec(7x)
u = 7x, so du/dx = 7
Therefore the answer is sec(7x)tan(7x) * 7 or
7 sec(7x)tan(7x)
d/dx csc(u) = -csc(u)cot(u) du/dx
Example:
d/dx csc(18x)
u = 18x, so du/dx = 18
Therefore the answer is -csc(18x)cot(18x) * 18 or
-18 csc(18x)cot(18x)
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