Check the solution to "Find the 100th derivative of y=ex" - Plainmath

kuCAu

Answered question

2021-04-28

Find the

100^{t h}

derivative of

y = e^{x}

Answer & Explanation

faldduE

Skilled2021-04-30Added 109 answers

Step 1 : Analysis
Given :
To determine the

100^{t h}

derivative of

y = e^{x}

Step 2 : Simplification
The first derivative is

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

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

The second derivative is

\frac{d^{2} y}{{d x}^{2}} = \frac{d}{d x} (e^{x})

\frac{d^{2} y}{{d x}^{2}} = e^{x}

The third derivative is

\frac{d^{3} y}{{d x}^{3}} = \frac{d}{d x} (e^{x})

\frac{d^{3} y}{{d x}^{3}} = e^{x}

Step 3 : Solution
Since we know that derivative of

e^{x}

is always remain the same

e^{x}

.
Therefore
The

100^{t h}

derivative is

\frac{d^{100} y}{{d x}^{100}} = \frac{d}{d x} (e^{x})

\frac{d^{100} y}{{d x}^{100}} = e^{x}

The

100^{t h}

derivative of

y = e^{x} i s e^{x}

.

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