Derivatives: check my answers please

Apr 2010
29
0
Find the derivatives

#1) \(\displaystyle y=(a^2-5a)^{2010}\)


My Answer: \(\displaystyle 2010(a^2-5a)^{2009}(2a-5)\)


#2) \(\displaystyle g(x)=cos(PiX^2)\)


My Answer: \(\displaystyle -2PiX Sin(PiX^2)\)


#3) \(\displaystyle {z^2-z} / {3z+2}\)


My Answer: \(\displaystyle (2z-1) - (3z^2-3z) / 3z+2\)
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
Find the derivatives

#1) \(\displaystyle y=(a^2-5a)^{2010}\)


My Answer: \(\displaystyle 2010(a^2-5a)^{2009}(2a-5)\)


#2) \(\displaystyle g(x)=cos(PiX^2)\)


My Answer: \(\displaystyle -2PiX Sin(PiX^2)\)


#3) \(\displaystyle {z^2-z} / {3z+2}\)


My Answer: \(\displaystyle (2z-1) - (3z^2-3z) / 3z+2\)
1 and 2 are correct.
 
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Apr 2010
29
0
Is 3 not simplified or or where did i go wrong?
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
\(\displaystyle \frac{dy}{dz}\bigg[\frac{z^2-z}{3z+2}\bigg]=\frac{uv'-u'v}{v^2}=\frac{2z-1}{3z+2}-\frac{3(z^2-z)}{(3z+2)^2}\)