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Zielflug [23.3K]
3 years ago
9

Write the expression as a single natural logarithm. 3 In 5

Mathematics
1 answer:
Vaselesa [24]3 years ago
4 0
Whould you like to cash app flip turn 10 into 100
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Differentiate y=x⁴(1-2x⁵)⁶(5-8x³)².​
Liula [17]

Step-by-step explanation:

Let y(x)=f(x)g(x)h(x) where

f(x) = x^4

g(x)= (1 -2x^5)^6

h(x)= (5 - 8x^3)^2

so that

y(x) = x^4(1 -2x^5)^6(5 - 8x^3)^2

Recall that the derivative of the product of functions is

y'(x)=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)

so taking the derivatives of the individual functions, we get

f'(x) = 4x^3

g'(x) = 6(1 - 2x^5)^5(-10x^4)

h'(x) = 2(5 - 8x^3)(-24x^2)

So the derivative of y(x) is given by

y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2 +  x^4 6(1 -2x^5)^5(-10x^4)(5 - 8x^3)^2 +  x^4(1 -2x^5)^6 2(5 - 8x^3)(-24x^2)

or

y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2

\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 60x^8(1 -2x^5)^5(5 - 8x^3)^2

\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 48x^6(1 -2x^5)^6 2(5 - 8x^3)

3 0
2 years ago
Determine the standard variation of the data below. (1, 2, 3, 4, 5)
Ne4ueva [31]
Calculate for the mean/ average of the given numbers:
 
                             μ = (1 + 2 + 3 + 4 + 5) / 5 = 3

Then, we calculate for the summation of the squares of differences of these numbers from the mean, S
 
                             S  = (1 - 3)² + (2 - 3)² + (3 - 3)² + (4 - 3)² + (5 - 3)²
                                S = 10

Divide this summation by the number of items and take the square root of the result to get the standard deviation.

                              SD = sqrt (10 / 5) = sqrt 2  
                                    SD = 1.41

Thus, the standard deviation of the given is equal to 1.41. 
              
                            
8 0
3 years ago
Read 2 more answers
How could I write the fractions 1/2 2/5 6/10 from least to greatest
guapka [62]
1/2=5/10
2/5=4/10
6/10
so from least to greatest will be : 2/5 1/2 6/10  :)))))
6 0
3 years ago
Reflection across y=x​
alexdok [17]
C= (-2,3) B=(-3,0) D=(-3,4) would be the reflection across the axis
5 0
3 years ago
Elliot uses 3/8 pound of clay to make a charm for a necklace. how much clay does he use to make 4 charms?
Lapatulllka [165]

Answer:

3/2 pound of clay is used

5 0
3 years ago
Read 2 more answers
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