What is the derivative of e^{x^2}y ?

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

What is the first derivative of e^{x^2}y ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int \frac{1}{3} x^{2} d x

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

\int \frac{2}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (\frac{1 - 3 x}{2 x + 1})

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