Solve x^3x^5/x^6

$$\frac { x ^ { 3 } x ^ { 5 } } { x ^ { 6 } }$$

Evaluate

$$x^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{x^{8}}{x^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 8 to get 2.

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{8}}{x^{6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 8 to get 2.

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

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

$$2x^{2-1}$$

Subtract 1 from 2.

$$2x^{1}$$

For any term t, t^{1}=t.

$$2x$$