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maw [93]
2 years ago
12

Please help :) it would be cool if you helped

Mathematics
1 answer:
kifflom [539]2 years ago
6 0

Answer:

Ummm

Step-by-step explanation:

So what do you need help with?

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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
The two functions below are used to represent the height of a rocket above the ground after it is launched. which rocket reaches
Bess [88]
<span>The rocket that will reach a greater distance above the ground at its maximum height is y = -4x</span>² + 80x. The answer is letter B. This is because of the coefficient presented in the x² term. The number -4 is much greater than -6. Graphing these equations into a graphing paper or excel, you would get a parabola. 
7 0
3 years ago
Simplify<br> (-4-8i)-(-1-3i)
AfilCa [17]
3 - 2i is the answer .
8 0
3 years ago
Anyone ? Need help. Thanks
NNADVOKAT [17]

Answer:

B.\:\: g(x)=4(2^x)

Step-by-step explanation:

The given function is f(x)=2^x.

If an exponential function is of the form; F(x)=a(b^x), then 0 will vertically shrink the base function f(x)=b^x

and a\:>\:1 will vertically stretch the graph by a units.

The correct answer is B.

7 0
3 years ago
Please help equation below
qaws [65]

Answer:

3y √21 + 2 y√15

Step-by-step explanation:

To simply, we open up the bracket

We have this as;

√(189y^2) + √60y

= 3y √21 + 2 y√15

7 0
2 years ago
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