1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Drupady [299]
3 years ago
10

What is partial derivative of z=(2x+3y)^10 with respect to x,y?

Mathematics
2 answers:
Andru [333]3 years ago
8 0

Answer:

Step-by-step explanation:

Given that z is a function of x,y

z=(2x+3y)^{10}

Partially differentiate wrt x and y separately to get

\dfrac\partial{\partial x}(2x+3y)^{10}=10(2x+3y)^9\times2=20(2x+3y)^9\\\dfrac\partial{\partial y}(2x+3y)^{10}=10(2x+3y)^9\times3=30(2x+3y)^9

maw [93]3 years ago
3 0
Not sure if you mean to ask for the first order partial derivatives, one wrt x and the other wrt y, or the second order partial derivative, first wrt x then wrt y. I'll assume the former.

\dfrac\partial{\partial x}(2x+3y)^{10}=10(2x+3y)^9\times2=20(2x+3y)^9

\dfrac\partial{\partial y}(2x+3y)^{10}=10(2x+3y)^9\times3=30(2x+3y)^9

Or, if you actually did want the second order derivative,

\dfrac{\partial^2}{\partial y\partial x}(2x+3y)^{10}=\dfrac\partial{\partial y}\left[20(2x+3y)^9\right]=180(2x+3y)^8\times3=540(2x+3y)^8

and in case you meant the other way around, no need to compute that, as z_{xy}=z_{yx} by Schwarz' theorem (the partial derivatives are guaranteed to be continuous because z is a polynomial).
You might be interested in
How do you grow your own equations
natita [175]
You can formulate your own equations by analyzing the given problem and its statements. You can do some illustrations so you can understand it better. Introduce some variables and the rest is algebra. For example:

An orange costs $2 while a banana costs $1.5. How many oranges and bananas do you have to buy such that the total cost would equal to $20. You bought a total of 12 fruits.

First, you have to introduce variables. Let 'x' be the number of oranges and 'y' be the number of bananas. One equation you can get from here is knowing the amount of total cost: 2x + 1.5y = 20. Then, the other equation would be knowing the amount of fruits: x+y=12. You have two unknowns and two equations. Hence, you can solve the problem. Solving them simultaneously, you would get that x=4 and y=8.
4 0
3 years ago
Write the slope intercept form of a line that passes<br> through (3, -2) and is 1 to y = x + 3.
zhuklara [117]

Answer:12

Step-by-step explanation:

8 0
3 years ago
it is known that the population proton of utha residnet that are members of the church of jesus christ 0l6 suppose a random samp
Lady_Fox [76]

Answer:

0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Proportion of 0.6

This means that p = 0.6

Sample of 46

This means that n = 46

Mean and standard deviation:

\mu = p = 0.6

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.6*0.4}{46}} = 0.0722

Probability of obtaining a sample proportion less than 0.5.

p-value of Z when X = 0.5. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.5 - 0.6}{0.0722}

Z = -1.38

Z = -1.38 has a p-value of 0.0838

0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.

8 0
3 years ago
Plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help me
Vaselesa [24]
Show another picture i cant see you
5 0
2 years ago
A.19.7<br> B.19.2<br> C.21.3<br> D.20.8
nadya68 [22]

Answer:

x = 180

Step-by-step explanation:

since straight lines are 180

(is it asking to find the area?)

5 0
2 years ago
Other questions:
  • A single die is rolled twice. The 36​ equally-likely outcomes are shown to the right.
    12·1 answer
  • Which of the following best describes the Aztec Empire before it was conquered? A. a small, complex civilization B. a small, pri
    14·2 answers
  • X divided by 4 = -7 What is x? Show your work​
    10·1 answer
  • Simplify i^15. (imaginary numbers to the 15th power)
    7·1 answer
  • Fill in the blanks: We are going to factor this quadratic, so we need two numbers that multiply to ___ and add to ___
    11·1 answer
  • -2x-2y=-8<br> -4x-8y=-20
    10·1 answer
  • Find side x, giving your answer to 1 decimal place.<br> 810<br> 7 cm<br> 40°<br> Х
    14·1 answer
  • What is the value of Z?
    10·1 answer
  • Marcos instaló un antivirus en su teléfono que se actualiza cada 4 días, otro en su Tablet que se actualiza cada 6 días y otro e
    15·1 answer
  • Rationalise the denominator of: (√3 + √2)/(√3-√2) = ?<br>​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!