Solve x^5*x^-2/x^4x^-5

$$\frac { x ^ { 5 } \times x ^ { - 2 } } { x ^ { 4 } x ^ { - 5 } }$$

Evaluate

$$x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and -2 to get 3.

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

To multiply powers of the same base, add their exponents. Add 4 and -5 to get -1.

$$\frac{x^{3}}{x^{-1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -1 from 3 to get 4.

$$x^{4}$$

Differentiate w.r.t. x

$$4x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and -2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}}{x^{4}x^{-5}})$$

To multiply powers of the same base, add their exponents. Add 4 and -5 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}}{x^{-1}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -1 from 3 to get 4.

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

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

$$4x^{4-1}$$

Subtract 1 from 4.

$$4x^{3}$$