Alaina's blog, 12 Sept 2010

This week we learned about the shortcuts to derivatives

and dealing with the derivative of sine and cosine.

First, the shortcut to derivatives is:

1. take the exponent
2. make it the constant
3. reduce the exponent by one
4. plug in

-if it is in a fraction, make it non-fraction by raising x to a negative exponent and then follow the steps.

Ex 1: 2x²+4

=2(2)x¹+4

=4x+4

Ex 2: ²/_3x

=(²/₃)(¹/_x)

=(²>/_3>>)(x^>-1)

=(²/₃>)(-1)(x^-2)

=(-²/₃)(¹>/_x^2sup>)

Second, taking the derivative of sine and cosine

-The rule for sine is

^d/_dx [sin x]=cos x

-The rule for cosine is

^d/_dx [cos x]=-sin x

Ex 1: ^d/_dx [2+2sin x]

=2+2cos x

Ex 2: ^d/_dx[1-cos x]

=1+sin x