Solve 1/3sqrt[3]{216}x^12

$$\frac { 1 } { 3 } \sqrt[ 3 ] { 216 } x ^ { 12 }$$

Evaluate

$$2x^{12}$$

Solution Steps

Calculate \sqrt[3]{216} and get 6.

$$\frac{1}{3}\times 6x^{12}$$

Multiply \frac{1}{3} and 6 to get 2.

$$2x^{12}$$

Differentiate w.r.t. x

$$24x^{11}$$

Steps Using Definition of a Derivative

Calculate \sqrt[3]{216} and get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3}\times 6x^{12})$$

Multiply \frac{1}{3} and 6 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{12})$$

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

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

Multiply 12 times 2.

$$24x^{12-1}$$

Subtract 1 from 12.

$$24x^{11}$$