The product rule for derivatives
product rule, sin(x), cosine(x), e(x), derivative
The Product Rule for derivatives is a way to find the derivative of a function H(x) that is the prodcut of two functions f(x) and g(x). So, if H(x)=f(x)g(x), then, the product rule says that the derivative of H, H'(x) is as follows:H'(x)=f'(x)g(x)+f(x)g'(x)
That is, the product of the derivative of the first function, times the second plus the first function times the derivative of the second function.
Example:
If we have a function H(x)=exsin(x), then, we can easily identify the two functions as f(x)=ex and g(x)=sin(x), then, applying the product rule, we see that:
H'(x)=exsin(x)+excos(x)=ex[sin(x)+cos(x)]
Note here that the derivative of ex is ex itself and the derivative of sin(x) is cos(x).
product rule, sin(x), cosine(x), e(x), derivative