Derivative of $$$- \frac{9 t}{100}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dt} \left(- \frac{9 t}{100}\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$ with $$$c = - \frac{9}{100}$$$ and $$$f{\left(t \right)} = t$$$:
$${\color{red}\left(\frac{d}{dt} \left(- \frac{9 t}{100}\right)\right)} = {\color{red}\left(- \frac{9 \frac{d}{dt} \left(t\right)}{100}\right)}$$Apply the power rule $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dt} \left(t\right) = 1$$$:
$$- \frac{9 {\color{red}\left(\frac{d}{dt} \left(t\right)\right)}}{100} = - \frac{9 {\color{red}\left(1\right)}}{100}$$Thus, $$$\frac{d}{dt} \left(- \frac{9 t}{100}\right) = - \frac{9}{100}$$$.
Answer
$$$\frac{d}{dt} \left(- \frac{9 t}{100}\right) = - \frac{9}{100}$$$A