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Popular >

derivative of xe^{2xy}

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

derivative of 9(3x+5^2)

\frac{d}{d x} (9 (3 x + 5)^{2})

limit as (x,y) approaches (0,3) of x^3y

(x, y) \to (0, 3) lim (x^{3} y)

derivative of ((x^3)^2)^2 derivative of

((x^{3})^{2})^{2}

(\partial)/(\partial x)(1/(y-1))

\frac{\partial}{\partial x} (\frac{1}{y - 1})

integral of e^{2x}*2x

\int e^{2 x} \cdot 2 x d x

Frequently Asked Questions (FAQ)

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