Solve x^2*x^12/x^7

$$\frac { x ^ { 2 } \cdot x ^ { 12 } } { x ^ { 7 } }$$

Evaluate

$$x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 12 to get 14.

$$\frac{x^{14}}{x^{7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 14 to get 7.

$$x^{7}$$

Differentiate w.r.t. x

$$7x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 12 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{14}}{x^{7}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 14 to get 7.

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

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

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

Subtract 1 from 7.

$$7x^{6}$$