# Taylor series problem (non-direct differentiation?)

1. Feb 18, 2014

### Loopas

I attached a picture of the problem from my online HW. I know how to solve the problem through direct differentiation, but that would too long to find the derivatives for this problem, and the problem actually suggests that I find another way. So my question is, what's the best way to solve this?

#### Attached Files:

• ###### hw.jpg
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2. Feb 18, 2014

### pasmith

Multiply the Taylor series of $\sin(7x)$ by $x^3$.

3. Feb 19, 2014

### Loopas

Thank you... wouldve never guessed it was so simple.