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

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

Differentiate w.r.t. x

$$2y\left(2x-3y\right)$$

Steps Using Derivative Rule for Sum

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}.

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

Multiply 2 times 2y.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

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

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

$$4yx-6y^{2}$$

Evaluate

$$3+2yx^{2}-6xy^{2}$$