Derivative of $$$3 t^{2} - 7$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dt} \left(3 t^{2} - 7\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dt} \left(3 t^{2} - 7\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(3 t^{2}\right) - \frac{d}{dt} \left(7\right)\right)}$$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 $$$c = 3$$$ and $$$f{\left(t \right)} = t^{2}$$$:
$${\color{red}\left(\frac{d}{dt} \left(3 t^{2}\right)\right)} - \frac{d}{dt} \left(7\right) = {\color{red}\left(3 \frac{d}{dt} \left(t^{2}\right)\right)} - \frac{d}{dt} \left(7\right)$$Apply the power rule $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ with $$$n = 2$$$:
$$3 {\color{red}\left(\frac{d}{dt} \left(t^{2}\right)\right)} - \frac{d}{dt} \left(7\right) = 3 {\color{red}\left(2 t\right)} - \frac{d}{dt} \left(7\right)$$The derivative of a constant is $$$0$$$:
$$6 t - {\color{red}\left(\frac{d}{dt} \left(7\right)\right)} = 6 t - {\color{red}\left(0\right)}$$Thus, $$$\frac{d}{dt} \left(3 t^{2} - 7\right) = 6 t$$$.
Answer
$$$\frac{d}{dt} \left(3 t^{2} - 7\right) = 6 t$$$A