Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![**Logarithmic Differentiation by Finding Y’**
The function given is:
\[ Y = \frac{19 \times e^{\sqrt{\sin(4x)}}}{(3x^2 + x^5)} \]
### Explanation of the Function and Steps for Logarithmic Differentiation:
1. **Identify the Function Components**:
- Numerator: \( 19 \times e^{\sqrt{\sin(4x)}} \)
- Denominator: \( 3x^2 + x^5 \)
2. **Apply Logarithmic Differentiation**:
- Take the natural logarithm (ln) of both sides to simplify the differentiation process.
- Use properties of logarithms to break down the expression:
\[ \ln(Y) = \ln(19) + \ln(e^{\sqrt{\sin(4x)}}) - \ln(3x^2 + x^5) \]
3. **Differentiate**:
- Apply the derivative rules (product rule, chain rule, etc.) to each term.
- Solve for \( Y' \), the derivative of \( Y \).
This presentation involves applying mathematical concepts and techniques, such as logarithmic differentiation, to analyze complex functions efficiently.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd390636-d92b-4083-92a5-4c40492431da%2F2bdeaf2f-3191-412f-836f-b5c1ba46e47b%2Fkoo0i3_processed.jpeg&w=3840&q=75)
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