Solve x^3-6x^2*8x

$$x ^ { 3 } - 6 x ^ { 2 } \times 8 x$$

Evaluate

$$-47x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{3}-6x^{3}\times 8$$

Multiply 6 and 8 to get 48.

$$x^{3}-48x^{3}$$

Combine x^{3} and -48x^{3} to get -47x^{3}.

$$-47x^{3}$$

Differentiate w.r.t. x

$$-141x^{2}$$

Steps Using Derivative Rule for Sum

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}.

$$3x^{3-1}+2\left(-48x\right)x^{2-1}$$

Subtract 1 from 3.

$$3x^{2}+2\left(-48x\right)x^{2-1}$$

Multiply 2 times -6\times 8x.

$$3x^{2}+\left(-96x\right)x^{2-1}$$

Subtract 1 from 2.

$$3x^{2}+\left(-96x\right)x^{1}$$

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

$$3x^{2}+\left(-96x\right)x$$