Solve x^8*x^8/x^2

$$\frac { x ^ { 8 } \cdot x ^ { 8 } } { x ^ { 2 } }$$

Evaluate

$$x^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 8 to get 16.

$$\frac{x^{16}}{x^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 16 to get 14.

$$x^{14}$$

Differentiate w.r.t. x

$$14x^{13}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 8 and 8 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{16}}{x^{2}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 16 to get 14.

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

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

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

Subtract 1 from 14.

$$14x^{13}$$