Solve 2x^2y-5xy-4x^2y+3-7xy-8

$$2 x ^ { 2 } y - 5 x y - 4 x ^ { 2 } y + 3 - 7 x y - 8$$

Differentiate w.r.t. x

$$-4xy-12y$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{2}y-5xy+3-7xy-8)$$

Combine -5xy and -7xy to get -12xy.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{2}y-12xy+3-8)$$

Subtract 8 from 3 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{2}y-12xy-5)$$

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}.

$$2\left(-2y\right)x^{2-1}+\left(-12y\right)x^{1-1}$$

Multiply 2 times -2y.

$$\left(-4y\right)x^{2-1}+\left(-12y\right)x^{1-1}$$

Subtract 1 from 2.

$$\left(-4y\right)x^{1}+\left(-12y\right)x^{1-1}$$

Subtract 1 from 1.

$$\left(-4y\right)x^{1}+\left(-12y\right)x^{0}$$

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

$$\left(-4y\right)x+\left(-12y\right)x^{0}$$

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

$$\left(-4y\right)x+\left(-12y\right)\times 1$$

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

$$\left(-4y\right)x-12y$$

Evaluate

$$-12xy-2yx^{2}-5$$