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BigorU [14]
3 years ago
6

Find expressions for the partial derivatives of the following functions:

Mathematics
1 answer:
nlexa [21]3 years ago
6 0

Answer:

Step-by-step explanation: partial derivative is the differentiation of one variable e.g. X while leaving the values of the other variable e.g. Y

These four questions A, B, C and D have different functions separated by commas. I will not assume the commas to be something else like a plus sign.

A. f(x) = g'(x).k(y) , g'(x) + h(y)

f(y) = k'(y).g(x) , g(x) + h'(y)

B. f(x) = g'x (x+y)

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

f(z) = h'z (y+z)

C. f(x) = f'x (xy) , f'x (zx)

f(y) = f'y (xy) , f'y (yz)

f(z) = f'z (yz) , f'z (zx)

D. f(x) = f'x (x) , g'(x) , h'x (x,y)

f(y) = h'x (x,y)

These are the partial derivative expressions for each variable in each function. You will need to pay a lot of attention to understand:

* while differentiating X alone, functions in Y which are separated by commas from the functions in X, are ignored totally because they are different questions

* In functions where X added to Y is in a bracket e.g. (x+y), to find the derivative of X, Y isn't thrown away because they are joined (by a plus sign) the derivative of X alone in this case would be f'x (x+y)

* f(x), just like g(x), simply means/represents a function in X hence f'(x) means the differentiation of all X-terms in that function

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posledela

Answer:

6

Step-by-step explanation:

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4x+7 = x+25

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7 0
3 years ago
X^2 -10x = 8 solve show work
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Answer:

Step-by-step explanation:

X^2-10x-8=0

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A scale drawing of a building shows 1 inch = 8 feet. How many feet are represented by 3 ¾ inches on the drawing?
Gennadij [26K]

Answer:

30 feet is represented by 3 3/4 inches on the drawing

Step-by-step explanation:

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1 inch = 8 feet

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3 3/4 inches = x feet

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6 0
3 years ago
What is the best approximation of the value of w? 1. 4 cm 4. 0 cm 6. 0 cm 7. 3 cm.
MrRissso [65]

To solve the problem we must know about Sine Rule.

<h3>What is Sine rule?</h3>

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}

where

  • Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
  • Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
  • Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

The value of w is 4.0 cm.

Given to us

  • VW = 3.3 cm,
  • ∠U = 31°,
  • ∠W = 39°,
<h3>Using the sine law,</h3>

\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}

Substitute the values,

\dfrac{Sin\ W}{w} = \dfrac{Sin\ U}{VW}

\dfrac{Sin\ 39^o}{w}=\dfrac{Sin\ 31^o}{3.3}

w=\dfrac{(Sin\ 39^o) \times 3.3}{Sin\ 31^o}

w = 4.03224 cm ≈ 4.0 cm

Hence, the value of w is 4.0 cm.

Learn more about Sine Rule:

brainly.com/question/17289163

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2 years ago
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