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allsm [11]
2 years ago
11

Differentiate with product rule​

Mathematics
1 answer:
Hitman42 [59]2 years ago
6 0

Answer:

{ \boxed{ \bf{ \frac{dy}{dx} = v \frac{du}{dx}  + u \frac{dv}{dx}  }}}

u = ( x + 1 )

v = ( 2x + 5 )²

{ \tt{ \frac{dy}{dx}  =  {(2x + 5) {}^{4} .(1) + (x + 1).(2)(2x + 5) {}^{3} } }} \\ =  { \tt{ {(2x + 5)}^{3} ((2x + 5) +(2x + 2) }} \\  = { \tt{ \frac{dy}{dx} =  {(2x + 5)}^{3}(4x + 7)  }}

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How many solutions are there to the functions? f(x)=3x+7
Andre45 [30]

Answer:

A. 0

Step-by-step explanation:

6 0
3 years ago
The equation 4x2 – 24x + 4y2 + 72y = 76 is equivalent to
DerKrebs [107]

Answer:

Option 4 is correct.

The equation 4x^2 -24x + 4y^2 + 72y = 76 is equivalent to 4(x-3)^2 + 4(y+9)^2 =436

Step-by-step explanation:'

Given equation: 4x^2 -24x + 4y^2 + 72y = 76

First group the terms with x and those with y;

(4x^2-24x)+(4y^2+72y) = 76

Next, we complete the squares.

We can do this by adding a third term such that the x terms and the y terms are perfect squares.

For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.

⇒4(x^2-6x) +4(y+18y) = 76

or

4(x^2 -6x +3^2 -3^2) + 4(y^2 +18y +9^2 -9^2) = 76

4(x^2-6x + 3^2) - 36 + 4(y^2+18y +9^2) - 324 = 76

4(x-3)^2 + 4(y+9)^2 - 360 =76

Add 360 on both sides we get;

4(x-3)^2 + 4(y+9)^2 =360 +76

Simplify:

4(x-3)^2 + 4(y+9)^2 =436

Therefore, the given equation is equivalent to 4(x-3)^2 + 4(y+9)^2 =436

5 0
3 years ago
Which of the following are mathematical sentences? Check all that applu
irina1246 [14]

Answer:

The correct options are:

A, B, and E.

Step-by-step explanation:

A mathematical sentence (or a mathematical statement) is a sentence that can be true or false.

This is the only criteria we need to check, now let's analyze each option.

A: 4 - d = 12

This can be true or false, for example, if d = 0 the sentence is false because:

4 - 0 = 12

4 = 12 is false.

and if d = -8 the sentence is true, because:

4 - (-8) = 12

4 + 8 = 12

12 = 12

is true.

B: 4 - V > 2

This sentence can be true or false, same reasoning as before, we can find values of V such that this is true or false.

C: 3 + 2

Now, here we can't say if this is true or false, so this is not a mathematical sentence.

D: 59

Same as before, this is just a number.

E: 6 + a = 13

This can be true or false, depending on the value of a, then this is a mathematical sentence.

F: 12*x

Here we can not say if this is true or false, so this is not a mathematical sentence.

The correct options are:

A, B, and E.

5 0
2 years ago
Study the red pre-image and the associated blue dilation image. The center of dilation is (2, 2).
lakkis [162]

Answer:

3

Step-by-step explanation:

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2 years ago
It is given that 2(3 + x) = 6 + 2x. This is an example of the ___________ property.
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Since when you multiply the numbers through, you see that the values are the same. Because of this, you can tell that you are demonstrating the distributive property.

Answer = C
6 0
2 years ago
Read 2 more answers
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