Solve x2/left(216^2right)^2

$$x \frac{ 2 }{ { \left( { 216 }^{ 2 } \right) }^{ 2 } }$$

Evaluate

$$\frac{x}{1088391168}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x\times \frac{2}{216^{4}}$$

Calculate 216 to the power of 4 and get 2176782336.

$$x\times \frac{2}{2176782336}$$

Reduce the fraction \frac{2}{2176782336} to lowest terms by extracting and canceling out 2.

$$x\times \frac{1}{1088391168}$$

Differentiate w.r.t. x

$$\frac{1}{1088391168} = 9.187873159955668 \times 10^{-10}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{2}{216^{4}})$$

Calculate 216 to the power of 4 and get 2176782336.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{2}{2176782336})$$

Reduce the fraction \frac{2}{2176782336} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{1}{1088391168})$$

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

$$\frac{1}{1088391168}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{1088391168}x^{0}$$

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

$$\frac{1}{1088391168}\times 1$$

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

$$\frac{1}{1088391168}$$