What is the derivative of x^2e^y ?

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

What is the first derivative of x^2e^y ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int s 4^{s} d s

\int_{0}^{\frac{π}{2}} (cos (x))^{2} d x

n = 1 \sum \infty 4^{\frac{1}{2 ^{n}}}

y = (2^{x})^{8}

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