# Thread: derivative of trig function using product rule

1. ## derivative of trig function using product rule

I have to differentiate 8x^2 sinx tanx

I'm not sure if I have to use the product rule twice or If i just use 8x^2 as a constant times sinx

2. ## Re: derivative of trig function using product rule

Originally Posted by neontiger94
I have to differentiate 8x^2 sinx tanx
If $y=f\cdot g\cdot h$ then $y^{\prime}=(f^{\prime}\cdot g+f\cdot g^{\prime})\cdot h+(f\cdot g)\cdot h^{\prime}$

3. ## Re: derivative of trig function using product rule

Originally Posted by Plato
If $y=f\cdot g\cdot h$ then $y^{\prime}=(f^{\prime}\cdot g+f\cdot g^{\prime})\cdot h+(f\cdot g)\cdot h^{\prime}$
Which becomes the easy-to-remember $f' \cdot g \cdot h + f \cdot g' \cdot h + f \cdot g \cdot h'$.

- Hollywood

4. ## Re: derivative of trig function using product rule

Originally Posted by hollywood
Which becomes the easy-to-remember $f' \cdot g \cdot h + f \cdot g' \cdot h + f \cdot g \cdot h'$.
I agree that it is easy-to-remember, but is it easy to understand how it comes about?

5. ## Re: derivative of trig function using product rule

You're right - it's definitely easier to see how $(f' \cdot g+f \cdot g') \cdot h+(f \cdot g) \cdot h$ comes about.