Question

Determine the derivatives of the function 𝑓(𝑥,𝑦)=2𝑥𝑦−5𝑥3𝑦2+5𝑥+7𝑦 and obtain the values at point (2,3)

275

likes
1373 views

Answer to a math question Determine the derivatives of the function 𝑓(𝑥,𝑦)=2𝑥𝑦−5𝑥3𝑦2+5𝑥+7𝑦 and obtain the values at point (2,3)

Expert avatar
Andrea
4.5
81 Answers
Para determinar as derivadas parciais da função 𝑓(𝑥,𝑦)=2𝑥𝑦−5𝑥^3𝑦^2+5𝑥+7𝑦 em relação a 𝑥 e 𝑦, podemos calcular as derivadas parciais de cada termo em relação a cada variável e então somá-las.

1. Derivada parcial em relação a 𝑥:
\frac{{\partial f}}{{\partial x}} = \frac{{\partial (2xy)}}{{\partial x}} - \frac{{\partial (5x^3y^2)}}{{\partial x}} + \frac{{\partial (5x)}}{{\partial x}} + \frac{{\partial (7y)}}{{\partial x}}
\frac{{\partial f}}{{\partial x}} = 2y - 15x^2y^2 + 5

2. Derivada parcial em relação a 𝑦:
\frac{{\partial f}}{{\partial y}} = \frac{{\partial (2xy)}}{{\partial y}} - \frac{{\partial (5x^3y^2)}}{{\partial y}} + \frac{{\partial (5x)}}{{\partial y}} + \frac{{\partial (7y)}}{{\partial y}}
\frac{{\partial f}}{{\partial y}} = 2x - 10x^3y + 7

Agora, para encontrar os valores no ponto (2,3), substituímos 𝑥=2 e 𝑦=3:

\frac{{\partial f}}{{\partial x}}\Big|_{(2,3)}=2(3)-15(2)^2(3)^2+5=-529

\frac{{\partial f}}{{\partial y}}\Big|_{(2,3)}=2(2)-10(2)^3(3)+7=-229

Portanto, as derivadas parciais da função 𝑓(𝑥,𝑦) em relação a 𝑥 e 𝑦 no ponto (2,3) são -169 e -469, respectivamente.

\textbf{Resposta:}\frac{{\partial f}}{{\partial x}}\Big|_{(2,3)}=-529\quad\text{e}\quad\frac{{\partial f}}{{\partial y}}\Big|_{(2,3)}=-229

Frequently asked questions (FAQs)
What is the measure of the central angle of a circle that intercepts an arc with a length of 60°?
+
What is the probability of rolling a prime number on a fair eight-sided die?
+
What is the value of angle θ, given that a = 10, b = 15, and c = 8 using the Sine Law?
+
New questions in Mathematics
A=m/2-t isolate t
1 + 1
-6n+5=-13
A normally distributed population has a mean of 118 with a standard deviation of 18. What score separates the lowest 72% of the distribution from the rest of the scores?
Let X be a discrete random variable with range {1, 3, 5} and whose probability function is f(x) = P(X = x). If it is known that P(X = 1) = 0.1 and P(X = 3) = 0.3. What is the value of P(X = 5)?
By differentiating the function f(x)=(x³−6x)⁷ we will obtain
Suppose 50% of the doctors and hospital are surgeons if a sample of 576 doctors is selected what is the probability that the sample proportion of surgeons will be greater than 55% round your answer to four decimal places
(2x+5)^3+(x-3)(x+3)
7/6-(-1/9)
2x+4x=
find f(x) for f'(x)=3x+7
suppose random variable x follows poisson distribution with expected value 3. what is variance of x?
A storage maker price is $2.50 per square feet. Find the price of a custom shed 4 yards long, and 5yards wide and 8 feet tall
1. A capital of $3,831 was lent, and it has produced interest of $840 from 05-12-2022 to 1-12-2023. At what annual simple interest rate was the capital lent?
-1%2F2x-4%3D18
For what values of m is point P (m, 1 - 2m) in the 2⁰ quadrant?
Find the zero of the linear function 8x + 24 = 0
X^X =49 X=?
A group of 17 people spent 9 days on vacation and spent R$776.34 on barbecue meat and the bill needs to be divided as follows: 6 people stayed for 9 days, 7 people stayed for 4 days, and 2 people stayed for 5 days and 2 people stayed 3 days, how much does each group have to pay for the days they stayed?
The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?