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Popular >

derivative of xe^{x^2-y}

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

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integral of 4/(sqrt(1-x^2))

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y^'=(xy^2+2x)/(y(2x^3+x^2+3))

y^{^{'}} = \frac{x y ^{2} + 2 x}{y ( 2 x ^{3} + x ^{2} + 3 )}

derivative of sin(3ln(x))derivative of

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x \to 1 lim (2 x^{3} - 4 x^{2} + x + 3)

Frequently Asked Questions (FAQ)

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