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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

\int - 3 tan (x) d x

y^{^{'}} = \frac{5 x ^{6} e ^{\frac{y}{x}} + x ^{4} y ^{2}}{x ^{5} y}

(e^{x} + 1)^{7}

8 y^{^{'}} + t y = 7

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