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Derivative of:
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Identical expressions
y=x^ four +e^-x
y equally x to the power of 4 plus e to the power of minus x
y equally x to the power of four plus e to the power of minus x
y=x4+e-x
y=x⁴+e^-x
Similar expressions
y=x^4-e^-x
y=x^4+e^+x

The derivative of the function/ y=x^4+e^-x

Derivative of y=x^4+e^-x

The solution

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 4    -x
x  + E

$$x^{4} + e^{- x}$$

x^4 + E^(-x)

Detail solution

Differentiate $x^{4} + e^{- x}$ term by term:
1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
2. Let $u = - x$ .
3. The derivative of $e^{u}$ is itself.
4. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- x\right)$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $-1$
  The result of the chain rule is:
  
  $- e^{- x}$
The result is: $4 x^{3} - e^{- x}$

The answer is:

$4 x^{3} - e^{- x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   -x      3
- e   + 4*x

$$4 x^{3} - e^{- x}$$

Simplify

The second derivative [src]

    2    -x
12*x  + e

$$12 x^{2} + e^{- x}$$

Simplify

The third derivative [src]

   -x       
- e   + 24*x

$$24 x - e^{- x}$$

Simplify

The graph

Derivative of y=x^4+e^-x