Is e^2 Considered a Constant in Differentiation?

[Ryuk1990]

Homework Statement

Derivative of f(x) = x³ + e²

Homework Equations

De^x = e^x

D constant = 0

The Attempt at a Solution

f'(x) = 3x² + 0?

Is e² treated as a constant?

 

[willem2]

Homework Statement

Derivative of f(x) = x³ + e²

Homework Equations

De^x = e^x

D constant = 0

The Attempt at a Solution

f'(x) = 3x² + 0?

Is e² treated as a constant?

Yes. Or you can use the chain rule. if u = f(x) = 2 and y = g(u) = $e^u$ then

$$\frac {dy} {dx} = \frac {dy} {du} \frac {du} {dx}$$

since $$\frac {du} {dx} = 0$$ $$\frac {dy} {dx} = 0$$.

 

[Mark44]

Homework Statement

Derivative of f(x) = x³ + e²

Homework Equations

De^x = e^x

D constant = 0

The Attempt at a Solution

f'(x) = 3x² + 0?

Is e² treated as a constant?

Not only is it treated as a constant, it is a constant. The derivative of any constant is zero. Period.

Using the chain rule certainly works, but it's definitely overkill, so not recommended.