Solve d/dxy(x^2+3)x^2

$$\frac{d}{d x } y ( { x }^{ 2 } +3) { x }^{ 2 }$$

Evaluate

$$6xy+4yx^{3}$$

Steps Using Derivative Rule for Sum

Use the distributive property to multiply y by x^{2}+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(yx^{2}+3y\right)x^{2})$$

Use the distributive property to multiply yx^{2}+3y by x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(yx^{4}+3yx^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$4yx^{4-1}+2\times 3yx^{2-1}$$

Subtract 1 from 4.

$$4yx^{3}+2\times 3yx^{2-1}$$

Multiply 2 times 3y.

$$4yx^{3}+6yx^{2-1}$$

Subtract 1 from 2.

$$4yx^{3}+6yx^{1}$$

For any term t, t^{1}=t.

$$4yx^{3}+6yx$$

Differentiate w.r.t. x

$$12yx^{2}+6y$$