Solve 3x^3-4x^3+x-8

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

Differentiate w.r.t. x

$$1-3x^{2}$$

Steps Using Derivative Rule for Sum

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

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

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}.

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

Multiply 3 times -1.

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

Subtract 1 from 3.

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

Subtract 1 from 1.

$$-3x^{2}+x^{0}$$

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

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

Evaluate

$$-x^{3}+x-8$$

Solution Steps

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

$$-x^{3}+x-8$$