Solve x^2*x^-3/x^-4*x

$$\frac { x ^ { 2 } \times x ^ { - 3 } } { x ^ { - 4 } \times x }$$

Evaluate

$$x^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

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

To multiply powers of the same base, add their exponents. Add -4 and 1 to get -3.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -3 from -1 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 2 and -3 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{-1}}{x^{-4}x})$$

To multiply powers of the same base, add their exponents. Add -4 and 1 to get -3.

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

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

$$2x$$