Home > Calculus > Summary of Differentiation Rules

What is the derivative of #c*(e^x)# where c is a constant?

Answer 1

Evelyn Agard

It is still #c*(e^x)#.

Multiplicative constants can always be removed from the expression when computing a derivative:

#d/dx[c*(e^x)]=c*d/dx[e^x]#

Since #d/dx[e^x]=e^x#, the derivative of the entire function is exactly the same as how it started:

#d/dx[c*(e^x)]=color(blue)(c*(e^x))#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Evelyn Agard

The derivative of c*(e^x) is c*(e^x).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 3

Christopher Allers

The derivative of ( c \cdot e^x ), where ( c ) is a constant, is simply ( c \cdot e^x ). This is because the derivative of ( e^x ) with respect to ( x ) is ( e^x ), and when multiplied by the constant ( c ), the derivative remains the same. Therefore, the derivative of ( c \cdot e^x ) is ( c \cdot e^x ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.