Solve (4x^2y+xy+6)+(-3x^2y+4xy-3)

$$( 4 x ^ { 2 } y + x y + 6 ) + ( - 3 x ^ { 2 } y + 4 x y - 3 )$$

Differentiate w.r.t. x

$$y\left(2x+5\right)$$

Steps Using Derivative Rule for Sum

Combine 4x^{2}y and -3x^{2}y to get x^{2}y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}y+xy+6+4xy-3)$$

Combine xy and 4xy to get 5xy.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}y+5xy+6-3)$$

Subtract 3 from 6 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}y+5xy+3)$$

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}.

$$2yx^{2-1}+5yx^{1-1}$$

Subtract 1 from 2.

$$2yx^{1}+5yx^{1-1}$$

Subtract 1 from 1.

$$2yx^{1}+5yx^{0}$$

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

$$2yx+5yx^{0}$$

For any term t except 0, t^{0}=1.

$$2yx+5y\times 1$$

For any term t, t\times 1=t and 1t=t.

$$2yx+5y$$

Evaluate

$$5xy+yx^{2}+3$$