What is the derivative of xe^{2y} ?

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

What is the first derivative of xe^{2y} ?

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

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Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot e^{2 y} + e^{2 y} \cdot 2 \frac{d y}{d x} x

Simplify

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

n = 0 \sum \infty (- 3 x + 1)^{n}

\int_{0}^{\frac{π}{9}} cos (3 x) d x

\frac{d}{d x} (\frac{1}{2} cos (2 x))

\int (10) d x

\frac{d}{d x} (\frac{5}{( 4 - 7 x ) ^{3}})

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