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Virty [35]
3 years ago
11

Use logarithmic differentiation to find dy/dx

Mathematics
1 answer:
liq [111]3 years ago
7 0

Answer:

dy/dx  =  (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]

Step-by-step explanation:

y = (x^2 - 3)^sinx

ln y = ln  (x^2 - 3)^sinx

ln y = sin x * ln (x^2 - 3)

1/y * dy/dx  =   sin x * {1 / (x^2 - 3)} * 2x + ln(x^2 - 3) * cos x

1/y dy/dx =  2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)

dy/dx  =   [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)] * y

dy/dx  =  (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]

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3 0
3 years ago
How do you solve this problem <br> 7= ln(x+5)
Gnesinka [82]
Answer:

x = 1091.63315843
<span>
Setting Up:

7 = ln ( x + 5 )

ln translates to "log" with an "e" as the base or subscript ( a small "e" at the bottom right of the "g" in log).

You take the base of the log and put it to the power of "7" ( "7" is the natural log of ( x + 5 ) in this problem ).

The value of which the logarithm is calculated is set equal to the base of the logarithm to the power of the calculated logarithm of the value.

e^7 = x + 5

Solving</span>:

e = 2.71828182846

Natural logarithms are logarithms to the base of the constant 'e'.

e^7 = x + 5    ( simplify e^7 )

<span>1096.63315843 = x + 5
</span>
Subtract 5 from each side.

1091.63315843 = x


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3 years ago
How many significant figures in 0.003010
Tamiku [17]
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