PLease help me <br> (put your answer in my comments please

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

China's population is 14.46×10^8. Marshall Islands' population is 602.5×10^2 . How many times larger is China's population than

Licemer1 [7]

I hope this helps you

8 0

3 years ago

1.In what ways did Egypt prosper during the reign of Hatshepsut? do your thing brainly!

Bond [772]

Answer:

She served as a queen, for Thutmose ll.

She served as queen alongside her husband, Thutmose II, but after his death, she claimed the role of pharaoh!. She reigned peace, she built temples and monuments, resulting in the flourishing of Egypt!

srry if this didn't help but I hope it did!

6 0

2 years ago

Kit bought a soft drink and a sandwich for $9.00. What was the price of each if the sandwich cost 3.5 times much as the soft dri

astra-53 [7]

Let the cost of the soft drink = C then the price of the sandwich was 3.5 times as much = 3.5C

And

C + 3.5C = Total Cost

C + 3.5C = 9

4.5C = 9 divide both sides by 4.5

C = 9/4.5 = $2.00 for the soft drink

And 3.5C = 3.5(2.00) = $7.00 cost of the sandwich

8 0

3 years ago

Read 2 more answers

Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P′Q′R′ has v

pav-90 [236]

lo siento de antemano! Necesito los puntos para hacer una publicación sobre mi amigo desaparecido. Ella desapareció y no puedo encontrarla. Ella se ha ido desde Halloween gracias por su comprensión. 8 9 028 los números son para covienes que estoy cosiendo el quistoion. Lo siento, nuevamente.

3 0

3 years ago

PLease help me (put your answer in my comments please