Solve 6/2x^2+3x^2-6x^2-x^3

$$\frac { 6 } { 2 } x ^ { 2 } + 3 x ^ { 2 } - 6 x ^ { 2 } - x ^ { 3 }$$

Evaluate

$$-x^{3}$$

Solution Steps

Divide 6 by 2 to get 3.

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

Combine 3x^{2} and 3x^{2} to get 6x^{2}.

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

Combine 6x^{2} and -6x^{2} to get 0.

$$-x^{3}$$

Differentiate w.r.t. x

$$-3x^{2}$$

Steps Using Definition of a Derivative

Divide 6 by 2 to get 3.

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

Combine 3x^{2} and 3x^{2} to get 6x^{2}.

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

Combine 6x^{2} and -6x^{2} to get 0.

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

The derivative of ax^{n} is nax^{n-1}.

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

Multiply 3 times -1.

$$-3x^{3-1}$$

Subtract 1 from 3.

$$-3x^{2}$$