Explained: "Find derivatives of the functions defined as follows:..."

expeditiupc

Answered question

2021-12-11

Find derivatives of the functions defined as follows:

y = - 8 e^{3 x}

Toni Scott

Beginner2021-12-12Added 32 answers

Step 1
Given:

y = - 8 e^{3 x}

Formula used:
If f(x) is any function and k is a constant then

\frac{d}{d x} [k f (x)] = k \frac{d}{d x} f (x)

\frac{d}{d x} [e^{g (x)}] = e^{g (x)} g^{'} (x)

Step 2
The objective is to find the derivative of the function
Thus the given function is

y = - 8 e^{3 x}

It is known that,
If f(x) is any function and k is a constant then

\frac{d}{d x} [k f (x)] = k \frac{d}{d x} f (x)

\frac{d}{d x} [e^{g (x)}] = e^{g (x)} g^{'} (x)

Step 3
On considering the expression,

\frac{d y}{d x} = \frac{d}{d x} (- 8 e^{3 x})

= - 8 \frac{d}{d x} e^{3 x}

= - 8 (e^{3 x}) \frac{d}{d x} (3 x)

= - 8 (e^{3 x}) 3

= - 24 e^{3 x}

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