How do you differentiate #y=5e^x+3#?

Answer 1

#d/dx(5e^x+3) = 5e^x#

This is a nice one to differentiate.

You can watch this Proof that shows why the derivative of #e^x# is just equal to #e^x#; then, we can just differentiate the rest of the equation.

The derivative of any constant is equal to zero since the slope of any constant value is zero (a straight horizontal line equal to that value).

Then we treat the exponential plus its coefficient using the Power Rule.

#d/dx(5e^x) = d/dx(5)*e^x+5*d/dx(e^x) = (0)*(e^x)+(5)*(e^x)# #=5e^x#

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Answer 2

Aurora Alvarado

To differentiate the function ( y = 5e^x + 3 ), you would apply the rules of differentiation. The derivative of ( e^x ) is ( e^x ), so when differentiating ( 5e^x ), you keep the coefficient ( 5 ) and differentiate ( e^x ) to get ( 5e^x ). Since the derivative of a constant is zero, the derivative of ( 3 ) is ( 0 ). Therefore, the derivative of ( y = 5e^x + 3 ) is ( \frac{dy}{dx} = 5e^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.