Answered: "Find derivatives of the function defined as follows...."

maduregimc

Answered question

2022-01-14

Find derivatives of the function defined as follows.

y = e^{- 8 x}

usaho4w

Beginner2022-01-15Added 39 answers

Step 1
We have to find derivatives of the function:

y = e^{- 8 x}

We know the formula of derivatives,

\frac{{d x}^{n}}{d x} = n x^{n - 1}

\frac{d x}{d x} = 1

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

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

Step 2
Finding derivatives of the given function with respect to x by applying above formula, we get

\frac{d y}{d x} = \frac{d e^{- 8 x}}{d x}

= e^{- 8 x} (\frac{d (- 8 x)}{d x})

= e^{- 8 x} (- 8 \frac{d x}{d x})

= e^{- 8 x} (- 8 \times 1)

= - 8 e^{- 8 x}

Hence, derivatives of the given function is

- 8 e^{- 8 x}

reinosodairyshm

Beginner2022-01-19Added 36 answers

y = e^{- 8 x}

\frac{d u^{n}}{d u} = n x^{n - 1}

\frac{d e f (x)}{d u} = e^{f (x)} \frac{d f (x)}{d u}

\frac{d y}{d} u = \frac{d e^{- 8 u}}{d u}

= e^{- 8 u} (\frac{d (- 8 u)}{d u})

= e^{- 8 u} (- 8 d \frac{u}{d} u)

= e^{- 8 u} (- 8 \times 1)

= - 8 e^{- 8 u}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?