The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]
The derivative of a function f(x) is the ratio of the change in f(x) to the change in x
The given function is:
[tex]f(x)=5^{2x}[/tex]
Let u = 2x
Find the derivative of u. That is, du/dx
du/dx = 2
f(x) = 5^u
[tex]\frac{df}{du} =5^ulnu[/tex]
Using the chain rule of derivative
[tex]\frac{df}{dx}=\frac{df}{du} \times\frac{du}{dx}[/tex]
[tex]\frac{df}{dx} =5^uln5 \times 2\\\\\frac{df}{dx} =2ln5(5^{2x})[/tex]
The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]
Learn more on the derivative of a function here: https://brainly.com/question/17035616
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