Solve 4^|0|x(1/4)^100

$$4 ^ { | 0 | } x ( \frac { 1 } { 4 } ) ^ { 100 }$$

Evaluate

$$\frac{x}{1606938044258990275541962092341162602522202993782792835301376}$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0 is 0.

$$4^{0}x\times \left(\frac{1}{4}\right)^{100}$$

Calculate 4 to the power of 0 and get 1.

$$1x\times \left(\frac{1}{4}\right)^{100}$$

Calculate \frac{1}{4} to the power of 100 and get \frac{1}{1606938044258990275541962092341162602522202993782792835301376}.

$$1x\times \frac{1}{1606938044258990275541962092341162602522202993782792835301376}$$

Multiply 1 and \frac{1}{1606938044258990275541962092341162602522202993782792835301376} to get \frac{1}{1606938044258990275541962092341162602522202993782792835301376}.

$$\frac{1}{1606938044258990275541962092341162602522202993782792835301376}x$$

Differentiate w.r.t. x

$$\frac{1}{1606938044258990275541962092341162602522202993782792835301376} = 6.223015277861141 \times 10^{-61}$$

Steps Using Definition of a Derivative

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0 is 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4^{0}x\times \left(\frac{1}{4}\right)^{100})$$

Calculate 4 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1x\times \left(\frac{1}{4}\right)^{100})$$

Calculate \frac{1}{4} to the power of 100 and get \frac{1}{1606938044258990275541962092341162602522202993782792835301376}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1x\times \frac{1}{1606938044258990275541962092341162602522202993782792835301376})$$

Multiply 1 and \frac{1}{1606938044258990275541962092341162602522202993782792835301376} to get \frac{1}{1606938044258990275541962092341162602522202993782792835301376}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1606938044258990275541962092341162602522202993782792835301376}x)$$

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

$$\frac{1}{1606938044258990275541962092341162602522202993782792835301376}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{1606938044258990275541962092341162602522202993782792835301376}x^{0}$$

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

$$\frac{1}{1606938044258990275541962092341162602522202993782792835301376}\times 1$$

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

$$\frac{1}{1606938044258990275541962092341162602522202993782792835301376}$$