Calculus Study Guide GSL

D/DX (SecX)

secxtanx

D/DX (TanX)

Sec²X

D/DX (SinX)

CosX

D/DX (CosX)

-sinx 

D/DX (cotx)

-Csc²x

D/DX (cscx)

-cscxcotx

Cosecant 

1/sinx.        Hyp/opp

Secant

1/Cos. hyp/adj

Cotangent

1/Tangent. adj/opp

Sin

opp/hyp

Cos

Adj/hyp

Tan

opp/adj

D/DX Sin^-1 (Inverse Sin)

1/ sqrt(1 - x² )

D/DX Cos^-1 (inverse Cos)

-1/ sqrt(1-x²)

D/DX Tan^-1 (Inverse Tan)

1 / 1+x²

When is the particle moving in the positive direction?

V(t) > 0

When is the particle moving in the negative direction?

V(t) < 0

What is the particles maximum velocity?

Largest v(t) value on # line. (positive)

what is the particles maximum speed?

Maximise absv of v(t)

When is the particle motionless (at rest) ?

v(t) = 0 

when is the particle moving with constant velocity?

v’(t) = 0

When is the acceleration negative?

Slope of v(t) is negative.

When is the acceleration positive?

slope of v(t) is positive.

When is the particle slowing down?

V(t) and slope of v(t) have opposite signs.

When is the particle speeding up?

v(t) and slope of v(t) match signs