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

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

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

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

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

x \frac{d y}{d x} + 2 y \frac{d y}{d x} + y

Solution steps

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

Apply the Product Rule:

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

f = y, g = x + y

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

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

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

Simplify

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

= x \frac{d y}{d x} + 2 y \frac{d y}{d x} + y

(3 n^{2}) (4 n^{2})

e^{- 3 l n (3)}

(5 x^{2} + x) (5 x^{2} + x)

83 \cdot 8

5 a^{2} b^{2} (3 ab - 5 a^{2} b^{2})

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