Mathematics: How to differentiate ?

How to differentiate ? - id14219828, marabic22

Ответ:

Alexis3456829

01.09.2021

Mathematics

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.

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

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Ответ:

paigedice8090

13.05.2021

Mathematics

Think of it as a ratio:
Volumes:
8pi : 64pi
Area:
16pi : x

For the volumes, going from 8pi to 64pi requires multiplying 8pi by 8; multiplying by 8, therefore, is the volumetric scale factor, but we want to find the s' area of the larger sphere from the s' area of the smaller one;
we need the s' area scale factor.
To get this, we need to cube root the volumetric scale factor and then square it so:
8^1/3 = 2
2^2 = 4
Area scale factor = 4
so the area of the larger sphere is:
16 * 4 = 64 cm^2

If you don't get the scale factor stuff leave a comment and I'll try my best to elaborate.

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