What is the derivative of y^2e^{xy-3} ?

The derivative of y^2e^{xy-3} is 2y(dy)/(dx)e^{xy-3}+e^{xy-3}(x(dy)/(dx)+y)y^2

What is the first derivative of y^2e^{xy-3} ?

The first derivative of y^2e^{xy-3} is 2y(dy)/(dx)e^{xy-3}+e^{xy-3}(x(dy)/(dx)+y)y^2

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\frac{d}{d x} (y^{2} e^{x y - 3})

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

Solution steps

\frac{d}{d x} (y^{2} e^{x y - 3})

Apply the Product Rule:

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

f = y^{2}, g = e^{x y - 3}

= \frac{d}{d x} (y^{2}) e^{x y - 3} + \frac{d}{d x} (e^{x y - 3}) y^{2}

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

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

= 2 y \frac{d y}{d x} e^{x y - 3} + e^{x y - 3} (x \frac{d y}{d x} + y) y^{2}

f (x) = 4 x y

(1 + x^{2}) d y = (y - cot^{- 1} (x)) d x

\int \frac{2}{1 + x} d x

y = x^{3}

\int_{- 1}^{1} (y^{2} - 2) - (e^{y}) d y

What is the derivative of y^2e^{xy-3} ?
The derivative of y^2e^{xy-3} is 2y(dy)/(dx)e^{xy-3}+e^{xy-3}(x(dy)/(dx)+y)y^2
What is the first derivative of y^2e^{xy-3} ?
The first derivative of y^2e^{xy-3} is 2y(dy)/(dx)e^{xy-3}+e^{xy-3}(x(dy)/(dx)+y)y^2