Solve 2^3x^-2^7

$$2 ^ { 3 } x ^ { - 2 ^ { 7 } }$$

Evaluate

$$\frac{8}{x^{128}}$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$8x^{-2^{7}}$$

Calculate 2 to the power of 7 and get 128.

$$8x^{-128}$$

Differentiate w.r.t. x

$$-\frac{1024}{x^{129}}$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{-2^{7}})$$

Calculate 2 to the power of 7 and get 128.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{-128})$$

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

$$-128\times 8x^{-128-1}$$

Multiply -128 times 8.

$$-1024x^{-128-1}$$

Subtract 1 from -128.

$$-1024x^{-129}$$