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Derivative of $$$4 t^{2}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dt} \left(4 t^{2}\right)$$$.
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 $$$c = 4$$$ and $$$f{\left(t \right)} = t^{2}$$$:
$${\color{red}\left(\frac{d}{dt} \left(4 t^{2}\right)\right)} = {\color{red}\left(4 \frac{d}{dt} \left(t^{2}\right)\right)}$$Apply the power rule $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ with $$$n = 2$$$:
$$4 {\color{red}\left(\frac{d}{dt} \left(t^{2}\right)\right)} = 4 {\color{red}\left(2 t\right)}$$Thus, $$$\frac{d}{dt} \left(4 t^{2}\right) = 8 t$$$.
Answer
$$$\frac{d}{dt} \left(4 t^{2}\right) = 8 t$$$A
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