Solve x-08^x-2^x/x

$$x-0 \frac{ { 8 }^{ x } - { 2 }^{ x } }{ x }$$

Evaluate

$$x$$

Short Solution Steps

Express 0\times \frac{8^{x}-2^{x}}{x} as a single fraction.

$$x-\frac{0\left(8^{x}-2^{x}\right)}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{xx}{x}-\frac{0\left(8^{x}-2^{x}\right)}{x}$$

Since \frac{xx}{x} and \frac{0\left(8^{x}-2^{x}\right)}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-0\left(8^{x}-2^{x}\right)}{x}$$

Do the multiplications in xx-0\left(8^{x}-2^{x}\right).

$$\frac{x^{2}}{x}$$

Cancel out x in both numerator and denominator.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Express 0\times \frac{8^{x}-2^{x}}{x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-\frac{0\left(8^{x}-2^{x}\right)}{x})$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx}{x}-\frac{0\left(8^{x}-2^{x}\right)}{x})$$

Since \frac{xx}{x} and \frac{0\left(8^{x}-2^{x}\right)}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx-0\left(8^{x}-2^{x}\right)}{x})$$

Do the multiplications in xx-0\left(8^{x}-2^{x}\right).

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

Cancel out x in both numerator and denominator.

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

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.

$$1$$