Solve (3x^2y-2x+1)+(4x^2y+6x-3)

$$( 3 x ^ { 2 } y - 2 x + 1 ) + ( 4 x ^ { 2 } y + 6 x - 3 )$$

Differentiate w.r.t. x

$$14xy+4$$

Steps Using Derivative Rule for Sum

Combine 3x^{2}y and 4x^{2}y to get 7x^{2}y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}y-2x+1+6x-3)$$

Combine -2x and 6x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}y+4x+1-3)$$

Subtract 3 from 1 to get -2.

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

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}.

$$2\times 7yx^{2-1}+4x^{1-1}$$

Multiply 2 times 7y.

$$14yx^{2-1}+4x^{1-1}$$

Subtract 1 from 2.

$$14yx^{1}+4x^{1-1}$$

Subtract 1 from 1.

$$14yx^{1}+4x^{0}$$

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

$$14yx+4x^{0}$$

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

$$14yx+4\times 1$$

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

$$14yx+4$$

Evaluate

$$4x+7yx^{2}-2$$