What is the derivative of (xy+1^2) ?

The derivative of (xy+1^2) is 2(xy+1)(x(dy)/(dx)+y)

What is the first derivative of (xy+1^2) ?

The first derivative of (xy+1^2) is 2(xy+1)(x(dy)/(dx)+y)

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\frac{d}{d x} ((x y + 1)^{2})

2 (x y + 1) (x \frac{d y}{d x} + y)

Solution steps

\frac{d}{d x} ((x y + 1)^{2})

Apply the chain rule:

2 (x y + 1) \frac{d}{d x} (x y + 1)

= 2 (x y + 1) \frac{d}{d x} (x y + 1)

\frac{d}{d x} (x y + 1) = x \frac{d y}{d x} + y

= 2 (x y + 1) (x \frac{d y}{d x} + y)

What is the derivative of (xy+1^2) ?
The derivative of (xy+1^2) is 2(xy+1)(x(dy)/(dx)+y)
What is the first derivative of (xy+1^2) ?
The first derivative of (xy+1^2) is 2(xy+1)(x(dy)/(dx)+y)