<h3>Answer:</h3>
<h3>Explanation:</h3>
It can work well to consider the function in parts. Define the following:
... a(x) = (1/2)ln(x^2+3)
... b(x) = x(4x^2-1)^3
Then the derivatives of these are ...
... a'(x) = (1/2)·1/(x^2 +3)·2x = x/(x^2+3)
... b'(x) = (4x^2 -1)^3 + 3x(4x^2 -1)^2·8x = (4x^2 -1)^2·(4x^2 -1 +24x^2)
... = (4x^2 -1)^2·(28x^2 -1)
___
<em>Putting the parts together</em>
f(x) = a(x)/b(x)
f'(x) = (b(x)a'(x) -a(x)b'(x))/b(x)^2 . . . . . rule for quotient of functions
Substituting values, we have
... f'(x) = (x(4x^2 -1)^3·x/(x^2 +3) -(1/2)ln(x^2 +3)·(4x^2 -1)^2·(28x^2 -1)) / (x(4x^2 -1)^3)^2
We can cancel (4x^2 -1)^2 from numerator and denominator. We can also eliminate fractions (1/2, 1/(x^2+3)). Then we have ...
... f'(x) = 2x^2(4x^2 -1) -(x^2 +3)ln(x^2 +3)·(28x^2 -1)/(2x^2·(x^2 +3)(4x^2 -1)^4))
Simplifying a bit, this becomes ...
... f'(x) = (8x^4 -2x^2 -ln(x^2 +3)·(28x^4 +83x^2 -3))/(2x^2·(x^2 +3)(4x^2 -1)^4))
Answer:
6x³y
Step-by-step explanation:
(2xy) * 3x²
We know that 2 * 3 = 6 and x * x² = x¹ * x² = x⁽¹⁺²) = x³ so the final answer is 6x³y.
Answer:
There is no table
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given
Required
Determine the missing angles
Since AB = AD, then:
--- Base angles of an isosceles triangle
Hence:
--- angles in a triangle
Collect Like Terms
--- angle on a straight line
Since ABC is isosceles, then:
--- base angle of isosceles
Lastly:
<em>See attachment</em>
The area of a trapezoid is
A = (1/2) h (b1 + b2)
where
h is the height
b1 is length of base 1
b2 is the length of base 2
We are given with the area and assuming that the trapezoid is isosceles, the length of base 1 is
b1 = 4 ft
If the height of the trapezoid is 4.5 feet, it ensures that the shed will fit inside the trapezoid patch of land. Therefore, the height of the trapezoid is 4.5 feet.