What is the derivative of (θ(e^θ)(2θ)) ?

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

What is the first derivative of (θ(e^θ)(2θ)) ?

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

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

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

Solution steps

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

Simplify

(x) (e^{x}) (2 x) : 2 e^{x} x^{2}

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

(a \cdot b) - (c \cdot d)

x - b x - y + b y

(\frac{d}{d t} (sin (2 t)))^{2}

\frac{2550}{17000}

27 x^{4} + 40 x^{4} + 3 0^{2}

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