Solve 4^-2x^6^0

$$4 ^ { - 2 } x ^ { 6 ^ { 0 } }$$

Evaluate

$$\frac{x}{16}$$

Solution Steps

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{1}{16}x^{6^{0}}$$

Calculate 6 to the power of 0 and get 1.

$$\frac{1}{16}x^{1}$$

Calculate x to the power of 1 and get x.

$$\frac{1}{16}x$$

Differentiate w.r.t. x

$$\frac{1}{16} = 0.0625$$

Steps Using Definition of a Derivative

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{16}x^{6^{0}})$$

Calculate 6 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{16}x^{1})$$

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{16}x)$$

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

$$\frac{1}{16}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{16}x^{0}$$

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

$$\frac{1}{16}\times 1$$

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

$$\frac{1}{16}$$