What is the derivative of y*e^x ?

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

What is the first derivative of y*e^x ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = y, g = e^{x}

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

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

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

\frac{d}{d x} (\frac{54}{( 1 + 3 x ) ^{3}})

y^{^{'}} = (1 - 2 t) y

\frac{d}{d x} (x cot (\frac{5}{x ^{2}}))

\frac{x ^{2}}{x - 6}

\frac{d}{d x} (\frac{2 cos ( 2 x ) - 1}{2 cos ( x )})

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