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Popular >

derivative of x*e^{xy}

Solution

\frac{d}{d x} (x \cdot 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 (cos^2(x)^x)

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

limit as x approaches 0-of x^3+3x+2

x \to 0 - lim (x^{3} + 3 x + 2)

derivative of (x-6/(7x^2e^x))

\frac{d}{d x} (\frac{x - 6}{7 x ^{2} e ^{x}})

e^xy*(dy)/(dx)=e^{-y}+e^{-3x-y}

e^{x} y \cdot \frac{d y}{d x} = e^{- y} + e^{- 3 x - y}

limit as x approaches 0+of (tan(2x))^2

x \to 0 + lim ((tan (2 x))^{2})

Frequently Asked Questions (FAQ)

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