Calculate the derivative of the function g(x)=e2x.
Nov 22, 2023
Calculate the derivative of the function g(x)=e2x.
Here is a Step-by-Step solution:
#step 1#
To calculate the derivative of the function g(x)=e2x, we will use the chain rule. The chain rule is a formula for computing the derivative of the composition of two or more functions.
#step 2#
Let's identify the outer function and the inner function in g(x). The outer function is the exponential function eu where u is the inner function, which in this case is 2x.
#step 3#
Now we apply the chain rule. The derivative of the outer function eu with respect to u is eu. Then we multiply this by the derivative of the inner function 2x with respect to x, which is 2.
#step 4#
Putting it all together, the derivative of g(x) is the derivative of the outer function times the derivative of the inner function: g′(x)=e2x⋅2
Answer
The derivative of the function g(x)=e2x is g′(x)=2e2x.
Key Concept
Chain Rule
Explanation
The chain rule was used to differentiate the composite function e2x, resulting in the derivative 2e2x.