SOLUTION: can someone help please My teacher is asking which of these statements is/are true select all that apply 1. if F(x)=f(x)*g(x), then F'(x)=f'(x)*g'(x) 2. if c is a constant, th

SOLUTION: can someone help please My teacher is asking which of these statements is/are true select all that apply 1. if F(x)=f(x)g(x), then F'(x)=f'(x)g'(x) 2. if c is a constant, th

Question 200743: can someone help please
My teacher is asking which of these statements is/are true select all that apply
1. if F(x)=f(x)*g(x), then F'(x)=f'(x)*g'(x)
2. if c is a constant, then d/dx(c*f(x))=c*d/dx(f(x))
3. if c is a constant, then d(c)/dx=0
4. if F(x)-f(x)+g(x), then F'(x)=f'(x)+g'(x)
5. if F(x)=f(x)*g(x), then F'(x)=f(x)*g'(x)+g(x)*f'(x)
6. none of these
7. if k is a real number, then d(x^k)/dx=kx^k-1
thanks a bunch

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
1. False. 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. True. The derivative is a linear operator. In other words, where "m" and "n" are constants.

3. True. 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 true. Once again, the derivative is a linear operator.

5. This is true (as this is the definition of the product rule).

6. False (since at least one is true, this is automatically false)

7. True. . Example:
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