Find the Derivative - d/dq 90q-(q^2)/100

$90 q - \frac{q^{2}}{100}$

By the Sum Rule, the derivative of $90 q - \frac{q^{2}}{100}$ with respect to $q$ is $\frac{d}{d q} [90 q] + \frac{d}{d q} [- \frac{q^{2}}{100}]$ .

$\frac{d}{d q} [90 q] + \frac{d}{d q} [- \frac{q^{2}}{100}]$

Evaluate $\frac{d}{d q} [90 q]$ .

Since $90$ is constant with respect to $q$ , the derivative of $90 q$ with respect to $q$ is $90 \frac{d}{d q} [q]$ .

$90 \frac{d}{d q} [q] + \frac{d}{d q} [- \frac{q^{2}}{100}]$

Differentiate using the Power Rule which states that $\frac{d}{d q} [q^{n}]$ is $n q^{n - 1}$ where $n = 1$ .

$90 \cdot 1 + \frac{d}{d q} [- \frac{q^{2}}{100}]$

Multiply $90$ by $1$ .

$90 + \frac{d}{d q} [- \frac{q^{2}}{100}]$

Evaluate $\frac{d}{d q} [- \frac{q^{2}}{100}]$ .

Since $- \frac{1}{100}$ is constant with respect to $q$ , the derivative of $- \frac{q^{2}}{100}$ with respect to $q$ is $- \frac{1}{100} \frac{d}{d q} [q^{2}]$ .

$90 - \frac{1}{100} \frac{d}{d q} [q^{2}]$

Differentiate using the Power Rule which states that $\frac{d}{d q} [q^{n}]$ is $n q^{n - 1}$ where $n = 2$ .

$90 - \frac{1}{100} (2 q)$

Multiply $2$ by $- 1$ .

$90 - 2 (\frac{1}{100}) q$

Combine $- 2$ and $\frac{1}{100}$ .

$90 + \frac{- 2}{100} q$

Combine $\frac{- 2}{100}$ and $q$ .

$90 + \frac{- 2 q}{100}$

Cancel the common factor of $- 2$ and $100$ .

Factor $2$ out of $- 2 q$ .

$90 + \frac{2 (- q)}{100}$

Cancel the common factors.

Factor $2$ out of $100$ .

$90 + \frac{2 (- q)}{2 (50)}$

Cancel the common factor.

$90 + \frac{2 (- q)}{2 \cdot 50}$

Rewrite the expression.

$90 + \frac{- q}{50}$

Move the negative in front of the fraction.

$90 - \frac{q}{50}$

Reorder terms.

$- \frac{q}{50} + 90$

Find the Derivative - d/dq 90q-(q^2)/100

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