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

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

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

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

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

2 x e^{k x} + e^{k x} k x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{\partial}{\partial x} (ln (4) e^{x})

4 x^{2} \cdot y^{^{'}} = y^{^{'}} + 9 x \cdot e^{- y}

\frac{\partial}{\partial x} (x^{13})

x^{2} - 5 x + 5

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

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