# What is the derivative of #t^2*2^t#?

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To find the derivative of ( t^2 \cdot 2^t ), you can use the product rule of differentiation. The product rule states that if ( f(t) ) and ( g(t) ) are differentiable functions, then the derivative of their product is given by:

[ (f(t) \cdot g(t))' = f'(t) \cdot g(t) + f(t) \cdot g'(t) ]

For ( f(t) = t^2 ) and ( g(t) = 2^t ), the derivatives are:

[ f'(t) = 2t ] [ g'(t) = 2^t \cdot \ln(2) ]

Using the product rule:

[ (t^2 \cdot 2^t)' = (2t \cdot 2^t) + (t^2 \cdot 2^t \cdot \ln(2)) ]

Therefore, the derivative of ( t^2 \cdot 2^t ) is:

[ 2t \cdot 2^t + t^2 \cdot 2^t \cdot \ln(2) ]

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