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3 years ago

Plz help i need to get this done

Mathematics

1 answer:

netineya [11]3 years ago

8 0

Answer:

$14.40

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please give brainliest.

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3 years ago

It's a 7th grade math problem

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Step-by-step explanation:

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2 years ago

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5/10 + 8/100 answer the problem

bekas [8.4K]

Answer:

The answer is 58/100

Step-by-step explanation:

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3 years ago

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How to solve this derivative. f(x)={ln(3x)}^2x with steps...

AysviL [449]

Rewrite f(x) as a nested exponential-logarithm expression :

$\left(\ln(3x)\right)^{2x} = \exp\left(\ln\left(\ln(3x)\right)^{2x}\right)$

(where $\exp(x) = e^x$ )

One of the properties of logarithms lets us drop the exponent as a coefficient:

$\exp\left(\ln\left(\ln(3x)\right)^{2x}\right) = \exp\left(2x\ln\left(\ln(3x)\right)\right)$

Now, by the chain rule, we have

$f(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \implies \\\\ f'(x) = \left(\exp\left(2x\ln\left(\ln(3x)\right)\right)\right)' \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2x\ln\left(\ln(3x)\right)\right)'$

By the product rule,

$f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left( (2x)' \ln\left(\ln(3x)\right) + 2x\left(\ln\left(\ln(3x)\right)\right)' \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left( 2\ln\left(\ln(3x)\right) + 2x\left(\ln\left(\ln(3x)\right)\right)' \right)$

By the chain rule again,

$f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + 2x \cdot \dfrac1{\ln(3x)} \cdot \left(\ln(3x)\right)' \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + \dfrac{2x}{\ln(3x)} \cdot \dfrac1{3x} \cdot (3x)' \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + \dfrac{2}{3\ln(3x)} \cdot 3 \right) \\\\ f'(x) = \exp\left(2x\ln\left(\ln(3x)\right)\right) \cdot \left(2\ln\left(\ln(3x)\right) + \dfrac{2}{\ln(3x)} \right)$

Then simplify this to

$f'(x) = \boxed{\left(\ln(3x)\right)^{2x} \left(2\ln\left(\ln(3x)\right) + \dfrac{2}{\ln(3x)} \right)}$

8 0

3 years ago