Derivative of x*ln(5x)
Answer
1+ln(5*x)
Derivative of x*ln(5x)
- Rule Used
- Product Rule
- Steps
- Identify a product of two functions of x in x*: use the product rule (uv)' = u'v + uv'. Each factor is differentiated once while the other is held as-is, then the two terms are added.
- Differentiate each factor and combine.
- Final answer: 1+
The derivative of x*ln(5*x) is 1+ln(5*x).
Instant step-by-step solution for x*ln(5x)
Share this result
Derivative of x*ln(5x) = 1+ln(5*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-xln5x
How to find the derivative of x*ln(5x)
To find the derivative of x*ln(5x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of x+1
Solve d/dx x+1
Derivative of x*sin(x)
Solve d/dx x*sin(x)
Derivative of x^2
Solve d/dx x^2
Derivative of x^2-1
Solve d/dx x^2-1
Derivative of x^2+1
Solve d/dx x^2+1
Derivative of x^4
Solve d/dx x^4
Derivative of ln(2x)
Solve d/dx ln(2x)
Derivative of ln(x)
Solve d/dx ln(x)
Derivative of x*ln(x)
Solve d/dx x*ln(x)
Frequently Asked Questions
What is the derivative of x*ln(5x)?▼
The derivative of x*ln(5x) is 1+ln(5*x).
How do you find the derivative of x*ln(5x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 1+ln(5*x).
Why is the derivative of x*ln(5x) equal to 1+ln(5*x)?▼
Because differentiation measures how a function changes — applying the rules to x*ln(5x) yields 1+ln(5*x). See the full step-by-step breakdown above.