Solve 2x^2-3x+8-2x^3+5x^2-6x

$$2 { x }^{ 2 } -3x+8-2 { x }^{ 3 } +5 { x }^{ 2 } -6x$$

Evaluate

$$8-9x+7x^{2}-2x^{3}$$

Solution Steps

Combine 2x^{2} and 5x^{2} to get 7x^{2}.

$$7x^{2}-3x+8-2x^{3}-6x$$

Combine -3x and -6x to get -9x.

$$7x^{2}-9x+8-2x^{3}$$

Differentiate w.r.t. x

$$-6x^{2}+14x-9$$

Steps Using Derivative Rule for Sum

Combine 2x^{2} and 5x^{2} to get 7x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}-3x+8-2x^{3}-6x)$$

Combine -3x and -6x to get -9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}-9x+8-2x^{3})$$

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}.

$$2\times 7x^{2-1}-9x^{1-1}+3\left(-2\right)x^{3-1}$$

Multiply 2 times 7.

$$14x^{2-1}-9x^{1-1}+3\left(-2\right)x^{3-1}$$

Subtract 1 from 2.

$$14x^{1}-9x^{1-1}+3\left(-2\right)x^{3-1}$$

Subtract 1 from 1.

$$14x^{1}-9x^{0}+3\left(-2\right)x^{3-1}$$

Multiply 1 times -9.

$$14x^{1}-9x^{0}-6x^{3-1}$$

Subtract 1 from 3.

$$14x^{1}-9x^{0}-6x^{2}$$

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

$$14x-9x^{0}-6x^{2}$$

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

$$14x-9-6x^{2}$$