What is the derivative of (x(x^2+y^2)) ?

The derivative of (x(x^2+y^2)) is 3x^2+2xy(dy)/(dx)+y^2

What is the first derivative of (x(x^2+y^2)) ?

The first derivative of (x(x^2+y^2)) is 3x^2+2xy(dy)/(dx)+y^2

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = x^{2} + y^{2}

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

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

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

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

Simplify

1 \cdot (x^{2} + y^{2}) + (2 x + 2 y \frac{d y}{d x}) x : 3 x^{2} + 2 x y \frac{d y}{d x} + y^{2}

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

- 8 (4 n - 1 = 2 (9 - 3 n))

(4 n^{2} + 2 n - 1) (2 n - 1)!

(- 7, - 5, 18) (y)

A (- 2, 3) y B (5, - 4)

What is the derivative of (x(x^2+y^2)) ?
The derivative of (x(x^2+y^2)) is 3x^2+2xy(dy)/(dx)+y^2
What is the first derivative of (x(x^2+y^2)) ?
The first derivative of (x(x^2+y^2)) is 3x^2+2xy(dy)/(dx)+y^2