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Tema [17]
4 years ago
7

I will mark brainiest is my answer is correct? I just got confuse because it saying do not simplify

Mathematics
1 answer:
sasho [114]4 years ago
6 0

Answer:

m^2 +my-my-y^2

Step-by-step explanation:

just dont simplify

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How to differentiate ?
Bas_tet [7]

Use the power, product, and chain rules:

y = x^2 (3x-1)^3

• product rule

\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2)}{\mathrm dx}\times(3x-1)^3 + x^2\times\dfrac{\mathrm d(3x-1)^3}{\mathrm dx}

• power rule for the first term, and power/chain rules for the second term:

\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(x-1)^2\times\dfrac{\mathrm d(3x-1)}{\mathrm dx}

• power rule

\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(3x-1)^2\times3

Now simplify.

\dfrac{\mathrm dy}{\mathrm dx} = 2x(3x-1)^3 + 9x^2(3x-1)^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2 \times (2(3x-1) + 9x) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2(15x-2)}

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.

On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

\ln(y) = \ln\left(x^2(3x-1)^3\right) \\\\ \ln(y) =  \ln\left(x^2\right) + \ln\left((3x-1)^3\right) \\\\ \ln(y) = 2\ln(x) + 3\ln(3x-1)

Differentiate both sides and you end up with the same derivative:

\dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac2x + \dfrac9{3x-1} \\\\ \dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \times x^2(3x-1)^3 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(15x-2)(3x-1)^2

7 0
2 years ago
How does tan 135 degrees compare to tan -135 degrees
Anna007 [38]
Evaluating the tangent function for the two values we obtain the following:
tan 135=tan(135+180)=tan 315=-1

next:
tan -135=tan(180-135)=tan 45=1
thus comparing the two we see that tan 135 is negative while tan -135 is positive
3 0
3 years ago
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Minchanka [31]

Answer:

Step-by-step explanation:

2k+10   | Both terms share the common factor two, so you can take it out (divide both terms by 2)

2(k+5)  | Now if you use the Distributive Property to double check, you get 2k+ 10 again

4 0
3 years ago
Hich points are reflections of each other across the y-axis?
Serhud [2]

Answer:

(- 7, - 3) and (7, - 3)

Step-by-step explanation:

The best way to do this is to sketch the graph...when dealing with reflection in the y axis, the value for y remains the same and the value for x becomes negative if it was positive or becomes positive if it was negative

4 0
3 years ago
Read 2 more answers
How do you do <br> 24 divided by 0.012
MariettaO [177]

Answer:

24 ÷ 0.012 =2000

Step-by-step explanation:

24 ÷ 0.012

= 2000

6 0
2 years ago
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