Solve x^2-2yx^3-3x^2+3x-3

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

Differentiate w.r.t. x

$$3-6yx^{2}-4x$$

Steps Using Derivative Rule for Sum

Multiply -1 and 2 to get -2.

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

Combine x^{2} and -3x^{2} to get -2x^{2}.

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

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}.

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

Multiply 2 times -2.

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

Subtract 1 from 2.

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

Multiply 3 times -2y.

$$-4x^{1}+\left(-6y\right)x^{3-1}+3x^{1-1}$$

Subtract 1 from 3.

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

Subtract 1 from 1.

$$-4x^{1}+\left(-6y\right)x^{2}+3x^{0}$$

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

$$-4x+\left(-6y\right)x^{2}+3x^{0}$$

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

$$-4x+\left(-6y\right)x^{2}+3\times 1$$

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

$$-4x+\left(-6y\right)x^{2}+3$$

Evaluate

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