Simple derivative of exponential function

In summary, the simple derivative of an exponential function is the derivative of the function without any additional terms or coefficients. To find the simple derivative, you can use the power rule. The simple derivative is equal to the slope of the tangent line at any point on the graph of the function, and can be used to determine the rate of change at a specific point. The difference between the simple derivative and the general derivative is that the general derivative takes into account additional terms and coefficients. The simple derivative can be negative, indicating a decrease in the function at that point on the graph.
  • #1
Jrlinton
134
1
1. Homework Statement
Find derivative of
y=e^(cos(t)+lnt)

Homework Equations

The Attempt at a Solution


So just using the chain rule:
y'=e^(cos(t)+lnt)*(-sin(t)+1/t)
The answer in the back of the book is
y'=e^(cos(t))*(1-tsin(t))
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Just trying to figure out where I went wrong or if these are just two forms of the same answer?
 
  • #3
The answers are identical. What is ##a^{b+c}## and what ##e^{\ln t}##?
 
  • #4
Thank you
 

FAQ: Simple derivative of exponential function

What is the simple derivative of an exponential function?

The simple derivative of an exponential function is the derivative of the function without any additional terms or coefficients.

How do you find the simple derivative of an exponential function?

To find the simple derivative of an exponential function, you can use the power rule, which states that the derivative of x^n is nx^(n-1). For example, the simple derivative of e^x would be e^x.

What is the relationship between the simple derivative of an exponential function and its graph?

The simple derivative of an exponential function is equal to the slope of the tangent line at any point on the graph of the function. This means that the derivative can be used to determine the rate of change of the function at a specific point.

What is the difference between the simple derivative and the general derivative of an exponential function?

The simple derivative only considers the exponential function itself, while the general derivative takes into account any additional terms or coefficients in the function. The general derivative is more complex and may require the use of logarithmic or other rules to find the derivative.

Can the simple derivative of an exponential function be negative?

Yes, the simple derivative of an exponential function can be negative. This would indicate that the function is decreasing at that point on the graph.

Similar threads

Replies
1
Views
1K
Replies
7
Views
1K
Replies
40
Views
626
Replies
11
Views
2K
Replies
4
Views
903
Back
Top