What is the derivative of (x(y)) ?

The derivative of (x(y)) is y+x(dy)/(dx)

What is the first derivative of (x(y)) ?

The first derivative of (x(y)) is y+x(dy)/(dx)

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = y

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

\frac{d x}{d x} = 1

= 1 \cdot y + \frac{d y}{d x} x

Simplify

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

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

(ln (x))^{n}

x^{2} + 2 x + x + 2

12 x^{- 6} + 7 x^{- 5} + x^{- 4}

\frac{d}{d x} (sin (x y))

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