Solve 4x^2y+8xy+11+-2x^2y+5xy+2

$$4 { x }^{ 2 } y+8xy+11+-2 { x }^{ 2 } y+5xy+2$$

Differentiate w.r.t. x

$$y\left(4x+13\right)$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}y+8xy+11+5xy+2)$$

Combine 8xy and 5xy to get 13xy.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}y+13xy+11+2)$$

Add 11 and 2 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}y+13xy+13)$$

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}.

$$2\times 2yx^{2-1}+13yx^{1-1}$$

Multiply 2 times 2y.

$$4yx^{2-1}+13yx^{1-1}$$

Subtract 1 from 2.

$$4yx^{1}+13yx^{1-1}$$

Subtract 1 from 1.

$$4yx^{1}+13yx^{0}$$

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

$$4yx+13yx^{0}$$

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

$$4yx+13y\times 1$$

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

$$4yx+13y$$

Evaluate

$$13xy+2yx^{2}+13$$