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