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Popular >

derivative of 2xe^y

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= 2 \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}

= 2 (\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}

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

Simplify

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

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\int_{- 3}^{3} \frac{12}{x ^{2} - 2 x - 35} d x

Frequently Asked Questions (FAQ)

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