# Math Help - An otherwise simple derivative problem...

1. ## An otherwise simple derivative problem...

Calculate:
d/dx[(e^x + xsin(x))/(tan(x))]

I got this far:
[tan(x) * e^x + 1cos(x)]-[e^x + xsin(x) * sex^2(x)]/[tan(x)]

But my book says it's supposed to be;
[tan(x) * e^x + sin(x) + xcos(x)]-[e^x + xsin(x) * sex^2(x)]/[tan(x)]

How come those things...?

2. ## Re: An otherwise simple derivative problem...

Originally Posted by Nervous
Calculate:
d/dx[(e^x + xsin(x))/(tan(x))]
this is the correct derivative ,,,

$\frac{\tan{x}\left(e^x + x\cos{x} + \sin{x}) - \sec^2{x}(e^x + x\sin{x})}{\tan^2{x}}$

note that the derivative of the numerator, $(e^x + x\sin{x})$, is $(e^x + x\cos{x} + \sin{x})$ ... you must use the product rule with $x\sin{x}$