Differentiation Summary Sheet
Basic Rules
Power Rule d/dx(x^n) = nx^(n-1)
Constant Rule d/dx(c) = 0
Constant Multiple Rule d/dx[c*f(x)] = c*f'(x)
Sum/Difference Rule d/dx[f(x) +/- g(x)] = f'(x) +/- g'(x)
Product Rule d/dx[f(x)*g(x)] = f'(x)g(x) + f(x)g'(x)
Quotient Rule d/dx[f(x)/g(x)] = (f'g - fg')/g^2
Chain Rule d/dx[f(g(x))] = f'(g(x)) * g'(x)
Standard Derivatives
x 1
x^n nx^(n-1)
sqrtx 1/(2sqrtx)
1/x -1/x^2
e^x e^x
a^x a^x * ln(a)
ln x 1/x
log_a x 1/(x ln a)
Trigonometric Functions
sin x cos x
cos x -sin x
tan x sec^2 x
cot x -csc^2 x
sec x sec x tan x
Basic Rules
Power Rule d/dx(x^n) = nx^(n-1)
Constant Rule d/dx(c) = 0
Constant Multiple Rule d/dx[c*f(x)] = c*f'(x)
Sum/Difference Rule d/dx[f(x) +/- g(x)] = f'(x) +/- g'(x)
Product Rule d/dx[f(x)*g(x)] = f'(x)g(x) + f(x)g'(x)
Quotient Rule d/dx[f(x)/g(x)] = (f'g - fg')/g^2
Chain Rule d/dx[f(g(x))] = f'(g(x)) * g'(x)
Standard Derivatives
x 1
x^n nx^(n-1)
sqrtx 1/(2sqrtx)
1/x -1/x^2
e^x e^x
a^x a^x * ln(a)
ln x 1/x
log_a x 1/(x ln a)
Trigonometric Functions
sin x cos x
cos x -sin x
tan x sec^2 x
cot x -csc^2 x
sec x sec x tan x
