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How do you find the derivative of #f(x)=5x-2e^x#?

Answer 1

#f'(x)=5-2e^x#

#f'(x)=(d(5x))/(dx)-(d(2e^x))/(dx)->#since there is only a subtraction operation, the separate parts of the function are able to be derived individually.

#(d(5x))/(dx)=5->#power rule

#(d(2e^x))/(dx)=2e^x->d/(dx)e^x=e^x#

#:.f'(x)=5-2e^x#

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Answer 2

William Abdalla

To find the derivative of ( f(x) = 5x - 2e^x ), you can use the sum rule and the derivative of the exponential function.

( \frac{d}{dx}(5x) = 5 ) (derivative of ( 5x )) ( \frac{d}{dx}(-2e^x) = -2e^x ) (derivative of ( -2e^x ))

So, the derivative of ( f(x) ) is ( f'(x) = 5 - 2e^x ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.