What is the derivative of x^2e^{x+3} ?

The derivative of x^2e^{x+3} is 2xe^{x+3}+e^{x+3}x^2

What is the first derivative of x^2e^{x+3} ?

The first derivative of x^2e^{x+3} is 2xe^{x+3}+e^{x+3}x^2

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\frac{d}{d x} (x^{2} e^{x + 3})

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

Solution steps

\frac{d}{d x} (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}

= \frac{d}{d x} (x^{2}) e^{x + 3} + \frac{d}{d x} (e^{x + 3}) x^{2}

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

\frac{d}{d x} (e^{x + 3}) = e^{x + 3}

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

y^{^{''}} - 2 y^{^{'}} + y = 1

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

ln (x + 9)

t \to 0 lim (e^{- 3 t})

\frac{3}{s ^{2} - 4}

What is the derivative of x^2e^{x+3} ?
The derivative of x^2e^{x+3} is 2xe^{x+3}+e^{x+3}x^2
What is the first derivative of x^2e^{x+3} ?
The first derivative of x^2e^{x+3} is 2xe^{x+3}+e^{x+3}x^2