Question 200743
1. <font color=red>False</font>. This is NEVER true and it is a misconception to many incoming calc students. Why? Well you first learn that if F(x)=f(x)+g(x), then F'(x)=f'(x)+g'(x). So many people wonder: "why not apply it to f(x)*g(x)?"



2. <font color=red>True</font>. The derivative is a linear operator. In other words, {{{(d/(dx))(m*f(x)+n*g(x))=m*(d/(dx))(f(x))+n*(d/(dx))(g(x))}}} where "m" and "n" are constants.


3. <font color=red>True</font>. Recall that a constant function graphs a horizontal line. Also, the slope of ANY horizontal line is zero.


4. I'm assuming you meant to write F(x)=f(x)+g(x). If so, then this is <font color=red>true</font>. Once again, the derivative is a linear operator.


5. This is <font color=red>true</font> (as this is the definition of the product rule).


6. <font color=red>False</font> (since at least one is true, this is automatically false)


7. <font color=red>True</font>. {{{d(x^k)/(dx)=k*x^(k-1)}}}. Example: {{{d(x^3)/(dx)=3x^(3-1)=3x^2}}}