"Find the derivatives of the functions p=3−t" was answered by our experts

facas9

Answered question

2021-10-06

Find the derivatives of the functions

p = \sqrt{3 - t}

Answer & Explanation

i1ziZ

Skilled2021-10-07Added 92 answers

Step 1
The rate of change in the value of the dependent variable with respect to the change in the value of the independent variable is known as the derivative. Here, the dependent variable is p and the independent variable is t, so we need to find

\frac{d p}{d t}

.
According to the power rule of differentiation,

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

and according to the chain rule of differentiation,

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

.
Step 2
Use the power rule and chain rule of differentiation to find the derivative of the function

p = \sqrt{3 - t}

with respect to t.

\frac{d p}{d t} = \frac{d}{d t} \sqrt{3 - t}

= \frac{d}{d t} {(3 - t)}^{\frac{1}{2}}

= \frac{1}{2} {(3 - t)}^{\frac{1}{2} - 1} \times \frac{d}{d t} (3 - t)

= \frac{1}{2 {(3 - t)}^{\frac{1}{2}}} \times (0 - 1)

= - \frac{1}{2 \sqrt{3 - t}}

Therefore, the derivative of

p = \sqrt{3 - t} i s - \frac{1}{2 \sqrt{3 - t}}

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