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Popular >

derivative of xe^{xy}

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

derivative of 8x^{-3}

\frac{d}{d x} (8 x^{- 3})

derivative of x/(11)-(11)/x derivative of

\frac{x}{11} - \frac{11}{x}

integral from 0 to 2*pi of sin(t)

\int_{0}^{2 \cdot π} sin (t) d t

derivative of 3x+x^2

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

integral of 4xcos(9x)

\int 4 x cos (9 x) d x

Frequently Asked Questions (FAQ)

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