# Thread: Using product rule to differentiate equations.

1. ## Using product rule to differentiate equations.

h(x) = sq.root(t) * (1-t^2)

and

f(x)=x^3 cos x

I know the answers, but I don't know how to differentiate with a square root involved or trig function involved. I need the work to show me what I'm suppose to do. Thanks!

2. ## Re: Using product rule to differentiate equations.

The derivative of cos(x) is -sin(x).

So f '(x) = (x^3)' * cos(x) + x^3*(cos(x))' ...

= (3x^2)cos(x) - sin(x)x^3

3. ## Re: Using product rule to differentiate equations.

Originally Posted by TheChaz
The derivative of cos(x) is -sin(x).

So f '(x) = (x^3)' * cos(x) + x^3*(cos(x))' ...

= (3x^2)cos(x) - sin(x)x^3
thanks!

4. ## Re: Using product rule to differentiate equations.

What about the square root problem?