I am working on Taylor Series and I believe one of the derivatives in the solution manual is wrong.

 

I am taking the derivative of [math] f(x) = \frac{x}{(1-x^2)^{(3/2)}} [/math]

 

I believe it is: [math] f'(x) = \frac{1+2x^2}{(1-x^2)^2} [/math]

 

but the answer key says it is: [math] f'(x) = \frac{1+2x^2}{(1-x^2)^{5/2}} [/math]

 

Can you check my math please.

I agree with the book's solution. I just worked it and got the same answer your solution manual has.

 

Can you show us what you had just before you simplified the equation down to your final answer? I think you may have made an error in simplification.

Remember that taking the derivative for polynomial functions will decrease the exponent by a full unit. In this case something is to the power -3/2, after taking the derivative it will have to be the the power -5/2. If you didn't get something to the -5/2 power, then you made a mistake. Use the product rule and the chain rule and you should get the result the book printed.