Solve 12x^5div6x^2

$$12 { x }^{ 5 } \div 6 { x }^{ 2 }$$

Evaluate

$$2x^{7}$$

Solution Steps

Divide 12x^{5} by 6 to get 2x^{5}.

$$2x^{5}x^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$2x^{7}$$

Differentiate w.r.t. x

$$14x^{6}$$

Steps Using Definition of a Derivative

Divide 12x^{5} by 6 to get 2x^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5}x^{2})$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{7})$$

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

$$7\times 2x^{7-1}$$

Multiply 7 times 2.

$$14x^{7-1}$$

Subtract 1 from 7.

$$14x^{6}$$