Calculus Examples

$r (t) = 110 - \frac{6 t (f t^{3})}{\min}$

Step 1

By the Sum Rule, the derivative of $110 - \frac{6 t (f t^{3})}{\min}$ with respect to $f$ is $\frac{d}{d f} [110] + \frac{d}{d f} [- \frac{6 t (f t^{3})}{\min}]$ .

$\frac{d}{d f} [110] + \frac{d}{d f} [- \frac{6 t (f t^{3})}{\min}]$

Step 2

Since $110$ is constant with respect to $f$ , the derivative of $110$ with respect to $f$ is $0$ .

$0 + \frac{d}{d f} [- \frac{6 t (f t^{3})}{\min}]$

Step 3

Since $- \frac{6}{\min}$ is constant with respect to $f$ , the derivative of $- \frac{6 t (f t^{3})}{\min}$ with respect to $f$ is $- \frac{6}{\min} \frac{d}{d f} [t (f t^{3})]$ .

$0 - \frac{6}{\min} \frac{d}{d f} [t (f t^{3})]$

Step 4

Subtract $\frac{6}{\min} \frac{d}{d f} [t (f t^{3})]$ from $0$ .

$- \frac{6}{\min} \frac{d}{d f} [t (f t^{3})]$