Solve x^4y^0/x^-2=

$$\frac { x ^ { 4 } y ^ { 0 } } { x ^ { - 2 } } =$$

Evaluate

$$x^{6}$$

Solution Steps

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

$$y^{0}x^{6}$$

Calculate y to the power of 0 and get 1.

$$1x^{6}$$

For any term t, t\times 1=t and 1t=t.

$$x^{6}$$

Differentiate w.r.t. x

$$6x^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(y^{0}x^{6})$$

Calculate y to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1x^{6})$$

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

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

Subtract 1 from 6.

$$6x^{5}$$