What is the derivative of R(t)=50t^2e^{-t}+8 ?

The derivative of R(t)=50t^2e^{-t}+8 is 50(-e^{-t}t^2+2e^{-t}t)

What is the first derivative of R(t)=50t^2e^{-t}+8 ?

The first derivative of R(t)=50t^2e^{-t}+8 is 50(-e^{-t}t^2+2e^{-t}t)

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derivative of

R (t) = 50 t^{2} e^{- t} + 8

50 (- e^{- t} t^{2} + 2 e^{- t} t)

Solution steps

\frac{d}{d t} (50 t^{2} e^{- t} + 8)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (50 t^{2} e^{- t}) + \frac{d}{d t} (8)

\frac{d}{d t} (50 t^{2} e^{- t}) = 50 (2 e^{- t} t - e^{- t} t^{2})

\frac{d}{d t} (8) = 0

= 50 (2 e^{- t} t - e^{- t} t^{2}) + 0

Simplify

= 50 (- e^{- t} t^{2} + 2 e^{- t} t)

\frac{d}{d x} (4 x^{3} - 2 x^{2})

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 3} e^{4 t}

(16 + x^{2}) (\frac{d y}{d x}) - 2 x y = 0

ln (\frac{x ^{2}}{3 - x})

\frac{d y}{d x} = 3 y^{\frac{2}{3}}

What is the derivative of R(t)=50t^2e^{-t}+8 ?
The derivative of R(t)=50t^2e^{-t}+8 is 50(-e^{-t}t^2+2e^{-t}t)
What is the first derivative of R(t)=50t^2e^{-t}+8 ?
The first derivative of R(t)=50t^2e^{-t}+8 is 50(-e^{-t}t^2+2e^{-t}t)