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RideAnS [48]
2 years ago
6

Answer the Following problem about derivatives.

Mathematics
1 answer:
White raven [17]2 years ago
4 0

The derivatives for the given functions are as follows:

a) -3.

b) -1.

c) 1.

d) 0.

<h3>What is the product rule for a derivative?</h3>

The product rule for a derivative is given as follows:

[f(x)g(x)]' = f'(x)g(x) + g'(x)f(x).

Hence, at x = 6, we have that:

[f(x)g(x)]'(6) = f'(6)g(6) + g'(6)f(6).

Replacing the values given in this problem, we have that the answer for item a is:

[f(x)g(x)]'(6) = f'(6)g(6) + g'(6)f(6) = 2(-1) - 1(1) = -2 - 1 = -3.

<h3>What is the quotient rule for a derivative?</h3>

The quotient rule for a derivative is given as follows:

\left(\frac{f(x)}{g(x)}\right)^{\prime} = \frac{f^{\prime}(x)g(x) - g^{\prime}(x)f(x)}{g(x)^2}

Hence, at x = 6, we have that:

\left(\frac{f(x)}{g(x)}\right)^{\prime}(6) = \frac{f^{\prime}(6)g(6) - g^{\prime}(6)f(6)}{g(6)^2}

Then the derivative in item b is:

[2(-1) - (-1)(1)]/[(-1)^2] = -1/1 = -1.

<h3>What is the derivative for the square root of a function?</h3>

Applying the chain rule, the derivative is given by:

(\sqrt{f(x)})^{\prime} = \frac{1}{2\sqrt{f(x)}}f^{\prime}(x)

Replacing at x = 6, the derivative for item c is given by:

1/2 x 2 = 1.

<h3>What is the derivative of a constant?</h3>

The derivative of a constant is of 0. In item d, the multiplication of f(6) by g'(6) results in a constant, hence the derivative is of 0.

More can be learned about derivative rules at brainly.com/question/25081524

#SPJ1

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Answer:

Difference= $3,090.15 in favor of compounded interest

Step-by-step explanation:

Giving the following information:

Present value (PV)= $8,500

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What is the radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0?
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Answer:

2 units

Step-by-step explanation:

The given equation of the circle is:

x^{2} + y^{2}+8x-6y+21=0

The general equation of the circle is:

x^{2} + y^{2}+2gx+2fy+c=0

Comparing the given equation with the general equation we can say:

g = 4

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The formula for radius of the circle is:

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Using these values of the given circle, we get:

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Therefore, the length of radius of the given circle is 2.

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