Solve 4-7x^3+6x^2+3x^3-3+2x^2

$$4 - 7 x ^ { 3 } + 6 x ^ { 2 } + 3 x ^ { 3 } - 3 + 2 x ^ { 2 }$$

Evaluate

$$1+8x^{2}-4x^{3}$$

Solution Steps

Combine -7x^{3} and 3x^{3} to get -4x^{3}.

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

Subtract 3 from 4 to get 1.

$$1-4x^{3}+6x^{2}+2x^{2}$$

Combine 6x^{2} and 2x^{2} to get 8x^{2}.

$$1-4x^{3}+8x^{2}$$

Differentiate w.r.t. x

$$4x\left(4-3x\right)$$

Steps Using Derivative Rule for Sum

Combine -7x^{3} and 3x^{3} to get -4x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4-4x^{3}+6x^{2}-3+2x^{2})$$

Subtract 3 from 4 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1-4x^{3}+6x^{2}+2x^{2})$$

Combine 6x^{2} and 2x^{2} to get 8x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1-4x^{3}+8x^{2})$$

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}.

$$3\left(-4\right)x^{3-1}+2\times 8x^{2-1}$$

Multiply 3 times -4.

$$-12x^{3-1}+2\times 8x^{2-1}$$

Subtract 1 from 3.

$$-12x^{2}+2\times 8x^{2-1}$$

Multiply 2 times 8.

$$-12x^{2}+16x^{2-1}$$

Subtract 1 from 2.

$$-12x^{2}+16x^{1}$$

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

$$-12x^{2}+16x$$