What is the (x^2e^{x+3})^' ?

The (x^2e^{x+3})^' is 2xe^{x+3}+e^{x+3}x^2

What is the first (x^2e^{x+3})^' ?

The first (x^2e^{x+3})^' is 2xe^{x+3}+e^{x+3}x^2

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(x^{2} e^{x + 3})^{^{'}}

2 x e^{x + 3} + e^{x + 3} x^{2}

Solution steps

(x^{2} e^{x + 3})^{'}

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = e^{x + 3}

= (x^{2})^{^{'}} e^{x + 3} + (e^{x + 3})^{^{'}} x^{2}

(x^{2})^{'} = 2 x

(e^{x + 3})^{'} = e^{x + 3}

= 2 x e^{x + 3} + e^{x + 3} x^{2}

y^{^{'}} = - 3 y + e^{- 2 x}, y (0) = 0

f (x) = \frac{2}{1 + x ^{2}}, h (x) = x^{2}

\frac{d y}{d x} = (\frac{( x y ) ^{2}}{8} + y^{2})

\frac{d ^{2}}{d x ^{2}} (ln (x))

y^{^{''}} + 4.5 y^{^{'}} = 0

What is the (x^2e^{x+3})^' ?
The (x^2e^{x+3})^' is 2xe^{x+3}+e^{x+3}x^2
What is the first (x^2e^{x+3})^' ?
The first (x^2e^{x+3})^' is 2xe^{x+3}+e^{x+3}x^2