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

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

Differentiate w.r.t. x

$$3x\left(3x+2\right)$$

Steps Using Derivative Rule for Sum

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

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

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}.

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

Multiply 3 times 3.

$$9x^{3-1}+2\times 3x^{2-1}$$

Subtract 1 from 3.

$$9x^{2}+2\times 3x^{2-1}$$

Multiply 2 times 3.

$$9x^{2}+6x^{2-1}$$

Subtract 1 from 2.

$$9x^{2}+6x^{1}$$

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

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

Evaluate

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

Solution Steps

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

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