Question

Solve with solution...no spam answers pls

Answer 1

Let's analyze Hannah's work, step-by-step, to see if she made any mistakes. 

In Step 1, Hannah wrote $\dfrac{d}{dx} (-3+8x)$  as the sum of two separate derivatives $\dfrac{d}{dx}(-3)+ \dfrac{d}{dx} (8x)$ using the sum rule.

This step is perfectly fine. 

In Step 2, $\dfrac{d}{dx}(8x)$ was kept as it is, and $\dfrac{d}{dx}(-3)$ was rewritten as $0$ using the constant rule.Indeed, according to the constant rule, the derivative of a constant number is equal to zero.

This step is perfectly fine. 

In Step 3, $\dfrac{d}{dx} (8x)$  was rewritten as $\dfrac{d}{dx}(8) \dfrac{d}{dx}(x)$ supposedly using the constant multiple rule.

The problem is that according to the constant multiple rule, $\dfrac{d}{dx}(8x)$ should be rewritten as $8 \dfrac{d}{dx}(x)$ and not as $\dfrac{d}{dx}(8)\dfrac{d}{dx}(x)$.  

Therefore, Hannah made a mistake in this step.

Answer 2

Step 3, it should have been 8*d/dx(x) which leads to

Step 4 = 8*1  which leads to

Step 5 = 8