What is the derivative of e^x{g}(x) ?

The derivative of e^x{g}(x) is e^x{g}(x)+derivative of {g}(x)e^x

What is the first derivative of e^x{g}(x) ?

The first derivative of e^x{g}(x) is e^x{g}(x)+derivative of {g}(x)e^x

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

e^{x} g (x) + \frac{d}{d x} (g (x)) e^{x}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = g (x)

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

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

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

\int 3 cos (x) + 3 x d x

\frac{\partial}{\partial x} (x e^{x y + 1})

\frac{\partial}{\partial y} (2 x sin (x^{2} y))

\frac{d}{d x} (5 x^{2} + 3 x - 2)

(- 8, - 14), (61, - 32)

What is the derivative of e^x{g}(x) ?
The derivative of e^x{g}(x) is e^x{g}(x)+derivative of {g}(x)e^x
What is the first derivative of e^x{g}(x) ?
The first derivative of e^x{g}(x) is e^x{g}(x)+derivative of {g}(x)e^x