Answer:
x = 38
Step-by-step explanation:
using the law of logarithms
• x = n ⇔ x = , hence
(2x - 12) = 3 ⇒ 2x - 12 = = 64
add 12 to both sides
2x = 76 ( divide both sides by 2 )
x = 38
Answer:
A≈1075.21
d Diameter
37
d
r
r
r
d
d
C
A
Using the formulas
A=
π
r
2
d=
2
r
Solving forA
A=
1
4
π
d
2
=
h1
4
π
37
2
≈
1075.21009
Step-by-step explanation:
Answer:
im really confused soryy that i cant help
The derivatives of the functions are listed below:
(a)
(b)
(c) f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)²
(d) f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)]
(e) f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶
(f)
(g)
(h) f'(x) = cot x + cos (㏑ x) · (1 / x)
<h3>How to find the first derivative of a group of functions</h3>
In this question we must obtain the <em>first</em> derivatives of each expression by applying <em>differentiation</em> rules:
(a)
- Given
- Definition of power
- Derivative of constant and power functions / Derivative of an addition of functions / Result
(b)
- Given
- Definition of power
- Derivative of a product of functions / Derivative of power function / Rule of chain / Result
(c) f(x) = (sin x - cos x) / (x² - 1)
- f(x) = (sin x - cos x) / (x² - 1) Given
- f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)² Derivative of cosine / Derivative of sine / Derivative of power function / Derivative of a constant / Derivative of a division of functions / Result
(d) f(x) = 5ˣ · ㏒₅ x
- f(x) = 5ˣ · ㏒₅ x Given
- f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)] Derivative of an exponential function / Derivative of a logarithmic function / Derivative of a product of functions / Result
(e) f(x) = (x⁻⁵ + √3)⁻⁹
- f(x) = (x⁻⁵ + √3)⁻⁹ Given
- f'(x) = - 9 · (x⁻⁵ + √3)⁻⁸ · (- 5) · x⁻⁶ Rule of chain / Derivative of sum of functions / Derivative of power function / Derivative of constant function
- f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶ Associative and commutative properties / Definition of multiplication / Result
(f)
- Given
- Rule of chain / Derivative of sum of functions / Derivative of multiplication of functions / Derivative of logarithmic functions / Derivative of potential functions
- Distributive property / Result
(g)
- Given
- Derivative of the subtraction of functions / Derivative of arccosine / Derivative of arctangent / Rule of chain / Derivative of power functions / Result
(h) f(x) = ㏑ (sin x) + sin (㏑ x)
- f(x) = ㏑ (sin x) + sin (㏑ x) Given
- f'(x) = (1 / sin x) · cos x + cos (㏑ x) · (1 / x) Rule of chain / Derivative of sine / Derivative of natural logarithm /Derivative of addition of functions
- f'(x) = cot x + cos (㏑ x) · (1 / x) cot x = cos x / sin x / Result
To learn more on derivatives: brainly.com/question/23847661
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Answer:
a = h-7
Step-by-step explanation:
h = a+7
Subtract 7 from each side
h-7 = a+7-7
h-7 =a