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37 Cards in this Set
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definition of the derivative

F'(x) = lim as h approaches 0
[f(x+h)  f(x)] / h 

derivative of a constant times a function

d/dx (k(u(x))) = k du/dx


Power Rule (variable raised to a constant)

d/dx (u^n) = nu^(n1) du/dx


The Sum Rule

d/dx (u+v) = du/dx + dv/dx


The Difference Rule

d/dx (uv) = du/dx  dv/dx


The Product Rule

d/dx (uv) = uv' + vu'


The Quotient Rule

d/dx (u/v) = [vu'  uv'] / v^2


The Chain Rule

dy/dx = dy/du * du/dx
or d/dx (f(g(x)) = f'(g(x))g'(x) 

The Derivative of the Sine

d/dx (sinu) = cosu du/dx


The Derivative of the Cosine

d/dx (cosu) = sinu du/dx


The Derivative of the Tangent

d/dx (tanu) = sec^2 u du/dx


The Derivative of the Cotangent

d/dx (cotu) = csc^2 u


The Derivative of the Secant

d/dx (secu) = secu tanu du/dx


The Derivative of the Cosecant

d/dx (cscu) = cscu cotu du/dx


The Derivative of the Inverse Sine

d/dx (Sin^1 u) = 1/sqrt(1u^2) du/dx


The Derivative of the Inverse Cosine

d/dx(Cos^1 u) = 1/sqrt(1u^2) du/dx


The Derivative of the Inverse Tangent

d/dx(Tan^1 u) = 1/(1+u^2) du/dx


The Derivative of the Inverse Cotangent

d/dx(Cot^1 u) = 1/(1+u^2) du/dx


The Derivative of the Inverse Secant

d/dx(Sec^1 u) = 1/(usqrt(u^2  1) du/dx


The Derivative of the Inverse Cosecant

d/dx(Csc^1 u) = 1/(usqrt(u^2  1) du/dx


The Derivative of the Natural Log

d/dx (ln u) = 1/u du/dx


The Derivative of the log to base a

d/dx (loga u) = 1/(u lna) du/dx


The Derivative of e raised to a variable

d/dx (e^u) = e^u du/dx


The Derivative of a constant raised to a variable

d/dx (a^u) = a^u lna du/dx


Pythagorean Identities

sin^2 x + cos^2 x = 1
tan^2 x +1 = sec^2 x 1 + cot^2 x = csc^2 x 

sin even/odd formula

sin (x) = sinx


cos even/odd formula

cos(x) = cosx


tan even/odd formula

tan(x) = tanx


csc even/odd formula

csc(x) = cscx


sec even/odd formula

sec(x) = secx


cot even/odd formula

cot(x) = cotx


double angle formula: sin(2x)

= 2sinx cosx


double angle formula: cos(2x)

= cos^2 x  sin^2 x
= 2cos^2 x  1 = 12sin^2 x 

half angle formula: cos^2 x

= (1/2)(1+cos(2x))


double angle formula: tan(2x)

= (2tanx)/(1tan^2 x)


half angle formula: sin^2 x

= (1/2)(1cos(2x))


half angle formula: tan^2 x

= (1cos(2x))/(1+cos(2x))
