SOLUTION: Hi all, Can someone please show me, with working; how to differentiate the following with respect to x. These are three seperate equations with seperate answers. 1. {{{y=3x^2 + 4

Algebra ->  Equations -> SOLUTION: Hi all, Can someone please show me, with working; how to differentiate the following with respect to x. These are three seperate equations with seperate answers. 1. {{{y=3x^2 + 4      Log On


   

Question 200580: Hi all, Can someone please show me, with working; how to differentiate the following with respect to x.
These are three seperate equations with seperate answers.
1. y=3x%5E2+%2B+4x+%2B+2
2. y=x%5E2%2Asqrt%28x%29+%2B+1%2Fsqrt%28x%29+-+cos%283x%29
3. y=e%5E3x+%28x%5E2+%2B+ln%28x%29%29
If someone could show me one or all 3 that would be great.
Thanks, -nick.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

From algebra, you need to know that 
1. sqrt%28u%29=u%5E%281%2F2%29 
2. 1%2F%28u%5En%29+=+u%5E%28-n%29
and from calculus you need to know that

3. For y=u%5En, then %28dy%29%2F%28dx%29=n%2Au%5E%28n-1%29%28%28du%29%2F%28dx%29%29

4. For y=cos%28u%29, then +%28dy%29%2F%28dx%29+=+-sin%28u%29%28%28du%29%2F%28dx%29%29

5. For y=e%5Eu, then %28dy%29%2F%28dx%29=%28e%5Eu%29%28%28du%29%2F%28dx%29%29

6. For y=ln%28u%29, then %28dy%29%2F%28dx%29=%28%28du%29%2F%28dx%29%29%2Fu

7. For y=u%2Av, then %28dy%29%2F%28dx%29=u%28%28dv%29%2F%28dx%29%29%2Bv%28%28du%29%2F%28dx%29%29


1. y=3x%5E2+%2B+4x+%2B+2
   %28dy%29%2F%28dx%29=6x%2B4 

2. y=x%5E2%2Asqrt%28x%29+%2B+1%2Fsqrt%28x%29+-+cos%283x%29
   y=%28x%5E2%29%28x%5E%281%2F2%29%29+%2B+1%2F%28x%5E%281%2F2%29%29+-+cos%283x%29
   y=x%5E%282%2B1%2F2%29%2Bx%5E%28-1%2F2%29-cos%283x%29
   y=x%5E%285%2F2%29%2Bx%5E%28-1%2F2%29-cos%283x%29
   
   %28dy%29%2F%28dx%29=%285%2F2%29x%5E%283%2F2%29-%281%2F2%29x%5E%28-3%2F2%29%2B3sin%283x%29

3. y=e%5E%283x%29+%28x%5E2+%2B+ln%28x%29%29
    
   %28dy%29%2F%28dx%29=e%5E%283x%29%282x%2B1%2Fx%29%2B3e%5E%283x%29%28x%5E2%2Bln%28x%29%29
   %28dy%29%2F%28dx%29=e%5E%283x%29%28%282x%2B1%2Fx%29%2B3%28x%5E2%2Bln%28x%29%29%29
   %28dy%29%2F%28dx%29=e%5E%283x%29%282x%2B1%2Fx%2B3x%5E2%2B3%2Aln%28x%29%29


Edwin