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3 years ago

If f(x) = f(x)g(x), where f and g have derivatives of all orders, show that f'' = f ''g + 2f 'g' + fg''.

1 answer:

5 0

Differentiating once, we have

$f'(x)=f'(x)g(x)+f(x)g'(x)$

Differentiating again,

$f''(x)=f''(x)g(x)+f'(x)g'(x)+f'(x)g'(x)+f(x)g''(x)$
$f''(x)=f''(x)g(x)+2f'(x)g'(x)+f(x)g''(x)$

as needed.

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Tresset [83]

By definition, two angles are supplementary if the sum of them is 180 degrees. In this case (see figure attached with the answer) the line AD is transversal to lines AB and DC. This is a proof of the Same-side interior angle theorem.

This theorem states that if we have two lines that are parallel and we intercept those two lines with a line that is transversal to both, same-side interior angles are formed, and also sum 180º, in other words, they are supplementary angles.

Then:

By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are same-side interior angles. Because AB and DC are parallel, the same-side interior angles must be supplementary by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.

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3 years ago

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kow [346]

Answer:

1/5 is not greater than 2/7 because 1/5 = 7/35 and 2/7 = 10/35.

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3 years ago

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this is part 2 and you just have to find the total area in sq ft and also answer how much material do you need to make 3 backpac

Lubov Fominskaja [6]

1. 1 1/8= 18/16

5/16*2= 10/16

4/16*2= 8/16

9/16= 9/16

1/2= 8/16

18/16 + 10/16 + 8/16 + 9/16 + 8/16= 53/16

Simplify:

4 & 5/16sq ft

2. All you do is multiply that by 3... so 4 & 5/16 = 53/16 53/16*3 = 159/16 = 9 & 15/16 sq ft

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3 years ago

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Juli2301 [7.4K]

Answer:

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Here is Laila’s graph from the previous screen.

lidiya [134]

Answer:

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Step-by-step explanation:

There is no need for any specific answers, but here is one that could logically work out. Since the graph is going left/down, it has a negative slope, so -1/3 would be reasonable. The graph doesn't cross the origin and crosses above it, so this equation must have a positive 'b' value. In this case, I chose 8. y=-1/3+8 could represent Laila's graph.

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