calculating derivative of 6e^x/sinx

[fry10fry10]

I need help calculating the derivative of 6e^x/sinx. I believe it is [sinx * 6e^x - sinx * cosx]/sin^2(x). Is this correct, can I simplify this further?

 

[galactus]

One way to go would be to rewrite as $\displaystyle 6e^{x}csc(x)$ and use the product rule instead of the quotient rule.

$\displaystyle \frac{d}{dx}[e^{x}csc(x)]=e^{x}(-csc(x)cot(x))+e^{x}csc(x)=\frac{e^{x}(sin(x)-cos(x))}{sin^{2}(x)}$

Just another way. Just don't forget the 6.

 

[fry10fry10]

One way to go would be to rewrite as $\displaystyle 6e^{x}csc(x)$ and use the product rule instead of the quotient rule.

$\displaystyle \frac{d}{dx}[e^{x}csc(x)]=e^{x}(-csc(x)cot(x))+e^{x}csc(x)=\frac{e^{x}(sin(x)-cos(x))}{sin^{2}(x)}$

Just another way. Just don't forget the 6.

Thanks I appreciate it.