To find the derivative of the function q2−3, we can use the power rule of differentiation.The power rule states that for any function of the form f(x)=xn, where n is a constant, the derivative is given by:ddx(xn)=n·xn−1In this case, our function is q2−3, where q is the independent variable.Using the power rule, we can differentiate each term separately:ddq(q2)−ddq(3)For the first term, q2, we apply the power rule with n=2:ddq(q2)=2·q2−1=2qThe derivative of the constant term, −3, is zero, as the derivative of a constant is always zero.Putting it all together, the derivative of the function q2−3 is:ddq(q2−3)=2q−0=2qTherefore, the derivative of q2−3 with respect to q is 2q.

Expert answers to "Derivative of q^2-3"

Mathabo Linala

Answered question

2022-07-25

Derivative of q^2-3

Answer & Explanation

Eliza Beth13

Skilled2023-05-31Added 130 answers

To find the derivative of the function

q^{2} - 3

, we can use the power rule of differentiation.
The power rule states that for any function of the form

f (x) = x^{n}

, where

n

is a constant, the derivative is given by:

\frac{d}{d x} (x^{n}) = n \cdot x^{n - 1}

In this case, our function is

q^{2} - 3

, where

q

is the independent variable.
Using the power rule, we can differentiate each term separately:

\frac{d}{d q} (q^{2}) - \frac{d}{d q} (3)

For the first term,

q^{2}

, we apply the power rule with

n = 2

\frac{d}{d q} (q^{2}) = 2 \cdot q^{2 - 1} = 2 q

The derivative of the constant term,

- 3

, is zero, as the derivative of a constant is always zero.
Putting it all together, the derivative of the function

q^{2} - 3

is:

\frac{d}{d q} (q^{2} - 3) = 2 q - 0 = 2 q

Therefore, the derivative of

q^{2} - 3

with respect to

q

2 q

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