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How do you use the chain rule to differentiate #f(x) = e^(4x+9)#?

Answer 1

Elijah Abram

Let #y = e^u# and #u = 4x + 9#.

#y' = e^u# and #u' = 4#

#f'(x)= e^u xx 4 = e^(4x + 9) xx 4 = 4e^(4x + 9)#

Hopefully this helps!

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Answer 2

Emilia Aguilar

To differentiate ( f(x) = e^{4x + 9} ) using the chain rule:

Identify the outer function and the inner function.
- The outer function is ( e^x ).
- The inner function is ( 4x + 9 ).
Differentiate the outer function with respect to the inner function.
- The derivative of ( e^x ) is ( e^x ).
Differentiate the inner function with respect to ( x ).
- The derivative of ( 4x + 9 ) is ( 4 ).
Multiply the results of steps 2 and 3.
- ( e^{4x + 9} ) * ( 4 ) = ( 4e^{4x + 9} ).

Thus, the derivative of ( f(x) = e^{4x + 9} ) is ( f'(x) = 4e^{4x + 9} ).

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Answer from HIX Tutor

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