Solve w^5x^3/w^5x^-4

$$\frac { w ^ { 5 } x ^ { 3 } } { w ^ { 5 } x ^ { - 4 } }$$

Evaluate

$$x^{7}$$

Solution Steps

Cancel out w^{5} in both numerator and denominator.

$$\frac{x^{3}}{x^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$x^{7}$$

Differentiate w.r.t. x

$$7x^{6}$$

Steps Using Definition of a Derivative

Cancel out w^{5} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}}{x^{-4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

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

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

Subtract 1 from 7.

$$7x^{6}$$