What is the first derivative of xg(x) ?

The first derivative of xg(x) is 2xg

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derivative of xg(x)

derivative of

xg (x)

2 xg

Solution steps

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

Simplify

xgx : x^{2} g

= \frac{d}{d x} (x^{2} g)

Treat

g

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= g \frac{d}{d x} (x^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= g \cdot 2 x^{2 - 1}

Simplify

= 2 xg

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

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

\frac{d y}{d x} = \frac{x e ^{3 x + y^{3}}}{y ^{2}}

\frac{d}{d x} ((3 x^{3} - 4) (- 4 x - 3))

4 x^{2} y^{^{'}} = y^{^{'}} + 9 x e^{- y}