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

The derivative of x^2e^{xy} is 2xe^{xy}+e^{xy}(y+x(dy)/(dx))x^2

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

The first derivative of x^2e^{xy} is 2xe^{xy}+e^{xy}(y+x(dy)/(dx))x^2

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int \frac{e ^{3 x}}{e ^{3 x} + 6} d x

\frac{d}{d θ} (a sin (θ))

\frac{d}{d x} (3 x y^{3})

y^{^{''}} = - 9 sin (5 x)

\frac{\partial}{\partial x} (\frac{2}{x} - n)

What is the derivative of x^2e^{xy} ?
The derivative of x^2e^{xy} is 2xe^{xy}+e^{xy}(y+x(dy)/(dx))x^2
What is the first derivative of x^2e^{xy} ?
The first derivative of x^2e^{xy} is 2xe^{xy}+e^{xy}(y+x(dy)/(dx))x^2