Solve x^7x^4/x^5

$$\frac { x ^ { 7 } x ^ { 4 } } { x ^ { 5 } }$$

Evaluate

$$x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 4 to get 11.

$$\frac{x^{11}}{x^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 11 to get 6.

$$x^{6}$$

Differentiate w.r.t. x

$$6x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 4 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{11}}{x^{5}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 11 to get 6.

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

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

$$6x^{6-1}$$

Subtract 1 from 6.

$$6x^{5}$$