Find dx/dt x=2t^2+t

Problem

d()/d(t)*(2*t^2+t)

Solution

1. Identify the function to be differentiated with respect to t which is x=2*t^2+t

2. Apply the power rule to the first term, 2*t^2 The power rule states that d(t^n)/d(t)=n*t^(n−1)

(d(2)*t^2)/d(t)=2⋅2*t^(2−1)

(d(2)*t^2)/d(t)=4*t

3. Apply the power rule to the second term, t Since t is t^1 the derivative is 1*t^0

d(t)/d(t)=1

4. Combine the results using the sum rule of differentiation.

d(x)/d(t)=4*t+1

Final Answer

d(x)/d(t)=4*t+1

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