Explained: "Find the derivatives of the functions r=120−403+104"

snowlovelydayM

Answered question

2021-10-06

Find the derivatives of the functions

r = \frac{12}{0} - \frac{4}{0^{3}} + \frac{1}{0^{4}}

Answer & Explanation

Anonym

Skilled2021-10-07Added 108 answers

Step 1
The rate of change in value of dependent variable with respect to the change in value of an independent variable is known as the derivative of the function. According to the quotient rule of differentiation,

\frac{d}{d x} (\frac{f (x)}{g (x)}) = \frac{f^{'} (x) g (x) - f (x) g^{'} (x)}{{(g (x))}^{2}}

Also, the differentiation of the expression of the form

x^{n} i s n x^{n - 1}

. So, we need to use the quotient rule of differentiation to find the derivative of the function.
Step 2
Using the quotient rule of differentiation, differentiate the function

r = \frac{12}{0} - \frac{4}{0^{3}} + \frac{1}{0^{4}}

with respect to θ as follows:

\frac{d r}{d 0} = \frac{d}{d 0} (\frac{12}{0} - \frac{4}{0^{3}} + \frac{1}{0^{4}})

= \frac{d}{d 0} (\frac{12}{0}) - \frac{d}{d 0} (\frac{4}{0^{3}}) + \frac{d}{d 0} (\frac{1}{0^{4}})

= \frac{0 - 12}{0^{2}} - \frac{0 - 4 \cdot 30^{2}}{0^{6}} + \frac{0 - 40^{3}}{0^{8}}

= - \frac{12}{0^{2}} + \frac{12}{0^{4}} - \frac{4}{0^{5}}

Therefore, the derivative of the function is

\frac{d r}{d 0} = - \frac{12}{0^{2}} + \frac{12}{0^{4}} - \frac{4}{0^{5}}

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