What is the (f(x)e^{g(x)})' ?

The (f(x)e^{g(x)})' is f'(x)e^{g(x)}+e^{g(x)}g'(x)f(x)

What is the first (f(x)e^{g(x)})' ?

The first (f(x)e^{g(x)})' is f'(x)e^{g(x)}+e^{g(x)}g'(x)f(x)

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(f (x) e^{g (x)})^{'}

f' (x) e^{g (x)} + e^{g (x)} g' (x) f (x)

Solution steps

(f (x) e^{g (x)})^{'}

Apply the Product Rule:

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

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

= f^{^{'}} (x) e^{g (x)} + (e^{g (x)})^{^{'}} f (x)

(e^{g (x)})^{'} = e^{g (x)} g^{'} (x)

= f^{^{'}} (x) e^{g (x)} + e^{g (x)} g^{^{'}} (x) f (x)

\frac{d}{d x} (x - x)

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

x \to 0 lim (\frac{1 - x}{x ^{2}})

y^{^{''}} + 4 y = 20

\int 5 x - x d x

What is the (f(x)e^{g(x)})' ?
The (f(x)e^{g(x)})' is f'(x)e^{g(x)}+e^{g(x)}g'(x)f(x)
What is the first (f(x)e^{g(x)})' ?
The first (f(x)e^{g(x)})' is f'(x)e^{g(x)}+e^{g(x)}g'(x)f(x)