Solve 3x^3-2x^2+5x-7-4x^2-3x+2

$$3 x ^ { 3 } - 2 x ^ { 2 } + 5 x - 7 - 4 x ^ { 2 } - 3 x + 2$$

Evaluate

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

Solution Steps

Combine -2x^{2} and -4x^{2} to get -6x^{2}.

$$3x^{3}-6x^{2}+5x-7-3x+2$$

Combine 5x and -3x to get 2x.

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

Add -7 and 2 to get -5.

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

Differentiate w.r.t. x

$$9x^{2}-12x+2$$

Steps Using Derivative Rule for Sum

Combine -2x^{2} and -4x^{2} to get -6x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}-6x^{2}+5x-7-3x+2)$$

Combine 5x and -3x to get 2x.

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

Add -7 and 2 to get -5.

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

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}.

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

Multiply 3 times 3.

$$9x^{3-1}+2\left(-6\right)x^{2-1}+2x^{1-1}$$

Subtract 1 from 3.

$$9x^{2}+2\left(-6\right)x^{2-1}+2x^{1-1}$$

Multiply 2 times -6.

$$9x^{2}-12x^{2-1}+2x^{1-1}$$

Subtract 1 from 2.

$$9x^{2}-12x^{1}+2x^{1-1}$$

Subtract 1 from 1.

$$9x^{2}-12x^{1}+2x^{0}$$

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

$$9x^{2}-12x+2x^{0}$$

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

$$9x^{2}-12x+2\times 1$$

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

$$9x^{2}-12x+2$$