Solved: "Which of the following functions are their own..." - Plainmath

Idilwsiw2

Answered question

2021-11-20

Which of the following functions are their own derivative?

y = e^{x} - 4 y = e^{x} y = e^{4} x y = 4 e^{x}

Answer & Explanation

Daniel Williams

Beginner2021-11-21Added 14 answers

Step 1
Let the first function

y = e^{x} - 4

\frac{d y}{d x} = \frac{d}{d x} (e^{x} - 4)

= \frac{d}{d x} (e^{x}) - \frac{d}{d x} (4)

= e^{x}

\neq y

let the second function

y = e^{x}

.

\frac{d y}{d x} = \frac{d}{d x} (e^{x})

= e^{x}

=y
Step 2
Let the third function

y = e^{4} x

.

\frac{d y}{d x} = \frac{d}{d x} (e^{4} x)

= e^{4}

\neq y

Let the fourth function is

y = 4 e^{x}

.

\frac{d y}{d x} = \frac{d}{d x} (4 e^{x})

= 4 e^{x}

=y
Therefore,

e^{x} and 4 e^{x}

are their own derivatives.

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