What is the derivative of ,xe^y ?

The derivative of ,xe^y is (,(1*e^y+e^y(dy)/(dx)x))

What is the first derivative of ,xe^y ?

The first derivative of ,xe^y is (,(1*e^y+e^y(dy)/(dx)x))

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

(, (1 \cdot e^{y} + e^{y} \frac{d y}{d x} x))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{y}

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

\frac{d x}{d x} = 1

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

= (, (1 \cdot e^{y} + e^{y} \frac{d y}{d x} x))

ln (x^{2} - 24) = x - y + 6

\int 4 cos^{2} (31 x) d x

\int_{1}^{2} x - x d x

\frac{\partial}{\partial x} (6 x^{8 y})

\frac{\partial}{\partial z} (cos (x))

What is the derivative of ,xe^y ?
The derivative of ,xe^y is (,(1*e^y+e^y(dy)/(dx)x))
What is the first derivative of ,xe^y ?
The first derivative of ,xe^y is (,(1*e^y+e^y(dy)/(dx)x))