Solve 12x^6:6x^2

$$12 x ^ { 6 } : 6 x ^ { 2 }$$

Evaluate

$$2x^{8}$$

Solution Steps

Divide 12x^{6} by 6 to get 2x^{6}.

$$2x^{6}x^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$2x^{8}$$

Differentiate w.r.t. x

$$16x^{7}$$

Steps Using Definition of a Derivative

Divide 12x^{6} by 6 to get 2x^{6}.

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

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{8})$$

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

$$8\times 2x^{8-1}$$

Multiply 8 times 2.

$$16x^{8-1}$$

Subtract 1 from 8.

$$16x^{7}$$