Solve -10+5xy-3x^2.7-xy+7x^2

$$-10+5xy-3 { x }^{ 2 } .7-xy+7 { x }^{ 2 }$$

Evaluate

$$4xy+\frac{49x^{2}}{10}-10$$

Solution Steps

Multiply 3 and 0.7 to get 2.1.

$$-10+5xy-2.1x^{2}-xy+7x^{2}$$

Combine 5xy and -xy to get 4xy.

$$-10+4xy-2.1x^{2}+7x^{2}$$

Combine -2.1x^{2} and 7x^{2} to get 4.9x^{2}.

$$-10+4xy+4.9x^{2}$$

Differentiate w.r.t. x

$$\frac{49x}{5}+4y$$

Steps Using Derivative Rule for Sum

Multiply 3 and 0.7 to get 2.1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10+5xy-2.1x^{2}-xy+7x^{2})$$

Combine 5xy and -xy to get 4xy.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10+4xy-2.1x^{2}+7x^{2})$$

Combine -2.1x^{2} and 7x^{2} to get 4.9x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10+4xy+4.9x^{2})$$

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}.

$$4yx^{1-1}+2\times 4.9x^{2-1}$$

Subtract 1 from 1.

$$4yx^{0}+2\times 4.9x^{2-1}$$

Multiply 2 times 4.9.

$$4yx^{0}+9.8x^{2-1}$$

Subtract 1 from 2.

$$4yx^{0}+9.8x^{1}$$

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

$$4yx^{0}+9.8x$$

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

$$4y\times 1+9.8x$$

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

$$4y+9.8x$$