# Derivative of e^(1+lnx): Solving for y

• Juwad
In summary, a derivative is a mathematical concept used to measure the rate of change of one quantity with respect to another. It is important because it helps us understand the behavior of functions and has various real-world applications. The process for finding derivatives involves using rules and formulas, and it has limitations in terms of well-defined functions and complexity. Some common applications of derivatives include optimization problems, finding maximum and minimum values, and calculating rates of change and velocity.
Juwad
hello,

i need some assistance on this problem:

y = e^(1+lnx)

1st. I brought down the (1+lnx) by using natural log on both sides.

lny*y'=(1+lnx)*lne
y'/y=(1/x)*1

y'=e^(1+lnx)*(1/x)

what do i do next?

$$e^{1+\ln x}=e^1e^{\ln x}=ex$$

thanks,!

## What is a derivative?

A derivative is a mathematical concept that represents the rate at which one quantity is changing with respect to another. It is commonly used to measure the slope of a curve at a specific point.

## Why is finding the derivative important?

Finding the derivative is important because it allows us to understand the behavior of a function and make predictions about its future values. It is also a fundamental tool in calculus and is used in many real-world applications such as physics, economics, and engineering.

## What is the process for finding the derivative?

The process for finding the derivative involves using a set of rules and formulas to calculate the slope of a curve at a given point. This can be done using the limit definition of a derivative or by using techniques such as the power rule, product rule, and chain rule.

## What are some common applications of derivatives?

Some common applications of derivatives include optimization problems, finding maximum and minimum values, and calculating rates of change and velocity. Derivatives are also used in physics to calculate acceleration and in economics to analyze supply and demand curves.

## Are there any limitations to finding derivatives?

Yes, there are some limitations to finding derivatives. For example, not all functions have a well-defined derivative at every point. Also, finding derivatives of complex or non-standard functions can be challenging and may require more advanced techniques.

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