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3 years ago

Vertical angles must be:

Mathematics

1 answer:

AlexFokin [52]3 years ago

3 0

Vertical angles are congruent (equal in measure) and they have the same vertex point.

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Differentiate x^2 e^x logx

zimovet [89]

Product rule:

$\dfrac{\mathrm d}{\mathrm dx}(x^2e^x\log x)$

$=\dfrac{\mathrm d(x^2)}{\mathrm dx}e^x\log x+x^2\dfrac{\mathrm d(e^x)}{\mathrm dx}\log x+x^2e^x\dfrac{\mathrm d(\log x)}{\mathrm dx}$

Power rule:

$\dfrac{\mathrm d(x^2)}{\mathrm dx}=2x$

The exponential function is its own derivative:

$\dfrac{\mathrm d(e^x)}{\mathrm dx}=e^x$

Assuming the base of $\log x$ is $e$ , its derivative is

$\dfrac{\mathrm d(\log x)}{\mathrm dx}=\dfrac1x$

But if you mean a logarithm of arbitrary base $b$ , we have

$y=\log_bx\implies x=b^y=e^{y\ln b}\implies1=e^{y\ln b}\ln b\dfrac{\mathrm dy}{\mathrm dx}$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{e^{-y\ln b}}{\ln b}=\dfrac1{b^y\ln b}$

$\implies\dfrac{\mathrm d(\log_bx)}{\mathrm dx}=\dfrac1{x\ln b}$

So we end up with

$2xe^x\log x+x^2e^x\log x+\dfrac{x^2e^x}x$

$=xe^x(2\log x+x\log x+1)$

8 0

3 years ago

Please answer !!!!!! Will mark brainliest !!!!!!!!

Inga [223]

Answer:

f(u) = 9/5

Step-by-step explanation:

u - 5 = -4(u - 1) Distribute on the right side

u - 5 = -4u + 4

+4u +4u Add 4u to both sides

5u - 5 = 4

+ 5 + 5 Add 5 to both sides

5u = 9 Divide both sides by 5

u = 9/5

3 0

3 years ago

Read 2 more answers

What is the area of the parallelogram?

Marizza181 [45]

Answer:

0.6

Step-by-step explanation:

3 0

3 years ago

15 16 17 18 19 Ancers please

kodGreya [7K]

15. 1hour 7minutes and 5seconds

4 0

3 years ago

Carpenter A charges $50 an hour. Carpenter B charges $20 to visit your home plus $45 for each hour. For how many hours will the

umka2103 [35]

Answer:

4 hours to pay the same amount

and aif you want a 3 hours work you should get carpenter A

Step-by-step explanation:

$50x = 20 + 45x \\ 5x = 20 \\ x = 4hours \\$

carpenter A for 3 hours:

$50 \times 3 = 150dollars \\$

carpenter B for 3 hours:

$20 + 45 \times 3 = 155dollars$

8 0

3 years ago