Solve x*(x^0)^5

$$x \times ( x ^ { 0 } ) ^ { 5 }$$

Evaluate

$$x$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 0 and 5 to get 0.

$$xx^{0}$$

To multiply powers of the same base, add their exponents. Add 1 and 0 to get 1.

$$x^{1}$$

Calculate x to the power of 1 and get x.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 0 and 5 to get 0.

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

To multiply powers of the same base, add their exponents. Add 1 and 0 to get 1.

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

Calculate x to the power of 1 and get x.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$