Solve x^2-6xy-3xy+99^2

$$x ^ { 2 } - 6 x y - 3 x y + 99 ^ { 2 }$$

Evaluate

$$x^{2}-9xy+9801$$

Solution Steps

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

$$x^{2}-9xy+99^{2}$$

Calculate 99 to the power of 2 and get 9801.

$$x^{2}-9xy+9801$$

Differentiate w.r.t. x

$$2x-9y$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-9xy+99^{2})$$

Calculate 99 to the power of 2 and get 9801.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-9xy+9801)$$

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}.

$$2x^{2-1}+\left(-9y\right)x^{1-1}$$

Subtract 1 from 2.

$$2x^{1}+\left(-9y\right)x^{1-1}$$

Subtract 1 from 1.

$$2x^{1}+\left(-9y\right)x^{0}$$

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

$$2x+\left(-9y\right)x^{0}$$

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

$$2x+\left(-9y\right)\times 1$$

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

$$2x-9y$$