Solve 2x^2y^2-3xy+4+left(5+7xy-3x^2y^2right)

$$2 { x }^{ 2 } { y }^{ 2 } -3xy+4+ \left( 5+7xy-3 { x }^{ 2 } { y }^{ 2 } \right)$$

Differentiate w.r.t. x

$$2y\left(2-xy\right)$$

Steps Using Derivative Rule for Sum

Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}y^{2}-3xy+9+7xy-3x^{2}y^{2})$$

Combine -3xy and 7xy to get 4xy.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}y^{2}+4xy+9-3x^{2}y^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}y^{2}+4xy+9)$$

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}.

$$2\left(-y^{2}\right)x^{2-1}+4yx^{1-1}$$

Multiply 2 times -y^{2}.

$$\left(-2y^{2}\right)x^{2-1}+4yx^{1-1}$$

Subtract 1 from 2.

$$\left(-2y^{2}\right)x^{1}+4yx^{1-1}$$

Subtract 1 from 1.

$$\left(-2y^{2}\right)x^{1}+4yx^{0}$$

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

$$\left(-2y^{2}\right)x+4yx^{0}$$

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

$$\left(-2y^{2}\right)x+4y\times 1$$

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

$$\left(-2y^{2}\right)x+4y$$

Evaluate

$$4xy-\left(xy\right)^{2}+9$$