What is the derivative of x^25e^x ?

The derivative of x^25e^x is 5(2xe^x+e^xx^2)

What is the first derivative of x^25e^x ?

The first derivative of x^25e^x is 5(2xe^x+e^xx^2)

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\frac{d}{d x} (x^{2} 5 e^{x})

5 (2 x e^{x} + e^{x} x^{2})

Solution steps

\frac{d}{d x} (x^{2} \cdot 5 e^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x^{2} e^{x})

Apply the Product Rule:

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

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

= 5 (\frac{d}{d x} (x^{2}) e^{x} + \frac{d}{d x} (e^{x}) x^{2})

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

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

= 5 (2 x e^{x} + e^{x} x^{2})

y^{3} - (6 x + 2) + 3 x y^{2} y^{^{'}} = 0

(x^{3} - 4 x)^{8}

\int x cos^{2} (x) d x

\frac{\partial}{\partial x} (x^{2} + y^{2} - 1)

\frac{d}{d x} (sec (2 x) tan (2 x))

What is the derivative of x^25e^x ?
The derivative of x^25e^x is 5(2xe^x+e^xx^2)
What is the first derivative of x^25e^x ?
The first derivative of x^25e^x is 5(2xe^x+e^xx^2)