Solve (8x^2y-9xy-7)+(-6x^2y+6xy+9)

$$( 8 x ^ { 2 } y - 9 x y - 7 ) + ( - 6 x ^ { 2 } y + 6 x y + 9 )$$

Differentiate w.r.t. x

$$y\left(4x-3\right)$$

Steps Using Derivative Rule for Sum

Combine 8x^{2}y and -6x^{2}y to get 2x^{2}y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}y-9xy-7+6xy+9)$$

Combine -9xy and 6xy to get -3xy.

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

Add -7 and 9 to get 2.

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

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}.

$$2\times 2yx^{2-1}+\left(-3y\right)x^{1-1}$$

Multiply 2 times 2y.

$$4yx^{2-1}+\left(-3y\right)x^{1-1}$$

Subtract 1 from 2.

$$4yx^{1}+\left(-3y\right)x^{1-1}$$

Subtract 1 from 1.

$$4yx^{1}+\left(-3y\right)x^{0}$$

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

$$4yx+\left(-3y\right)x^{0}$$

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

$$4yx+\left(-3y\right)\times 1$$

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

$$4yx-3y$$

Evaluate

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