Solve =3x^2-5x-2x*x+3-6x-2x^3

$$=3 { x }^{ 2 } -5x-2x \times x+3-6x-2 { x }^{ 3 }$$

Evaluate

$$3-11x+x^{2}-2x^{3}$$

Solution Steps

Multiply x and x to get x^{2}.

$$3x^{2}-5x-2x^{2}+3-6x-2x^{3}$$

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

$$x^{2}-5x+3-6x-2x^{3}$$

Combine -5x and -6x to get -11x.

$$x^{2}-11x+3-2x^{3}$$

Differentiate w.r.t. x

$$-6x^{2}+2x-11$$

Steps Using Derivative Rule for Sum

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}-5x-2x^{2}+3-6x-2x^{3})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-5x+3-6x-2x^{3})$$

Combine -5x and -6x to get -11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-11x+3-2x^{3})$$

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}.

$$2x^{2-1}-11x^{1-1}+3\left(-2\right)x^{3-1}$$

Subtract 1 from 2.

$$2x^{1}-11x^{1-1}+3\left(-2\right)x^{3-1}$$

Subtract 1 from 1.

$$2x^{1}-11x^{0}+3\left(-2\right)x^{3-1}$$

Multiply 1 times -11.

$$2x^{1}-11x^{0}-6x^{3-1}$$

Subtract 1 from 3.

$$2x^{1}-11x^{0}-6x^{2}$$

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

$$2x-11x^{0}-6x^{2}$$

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

$$2x-11-6x^{2}$$