Which one of the following statements is true? (5 points)

if f and g are differentiable, then the derivative with respect to x of the product of f of x and g of x equals the product of f prime of x and g prime of x .

the derivative with respect to x of the absolute value of the quantity x squared plus x equals the absolute value of the quantity 2 times x plus 1

if f and g are differentiable, then the derivative with respect to x of the square root of f of x equals the quotient of f of x and 2 times the square root of f prime of x .

none of these statements are true.

  None of these statements are true.

Step-by-step explanation:

a) The derivative of (fg)(x) is f'g +fg' according to the product rule for derivatives.

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b) The derivative of |x² +x| is a 3-part piecewise linear function equal to 2x+1 for |x+1/2| > 1/2, and equal to -2x-1 for |x+1/2| < 1/2. It is undefined for x=0 and x=1.

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c) for y = √f(x), y' = f'(x)/(2√f(x))

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

1. minimum

2. 6400

3. eight

hope this !