Solve 1/5x2.6=

$$\frac{ 1 }{ 5 } x2.6=$$

Evaluate

$$\frac{3x_{2}}{25}$$

Solution Steps

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}x_{2}\times \frac{3}{5}$$

Multiply \frac{1}{5} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{5\times 5}x_{2}$$

Do the multiplications in the fraction \frac{1\times 3}{5\times 5}.

$$\frac{3}{25}x_{2}$$

Differentiate w.r.t. x_2

$$0.12$$

Steps Using Definition of a Derivative

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(\frac{1}{5}x_{2}\times \frac{3}{5})$$

Multiply \frac{1}{5} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(\frac{1\times 3}{5\times 5}x_{2})$$

Do the multiplications in the fraction \frac{1\times 3}{5\times 5}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(\frac{3}{25}x_{2})$$

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

$$\frac{3}{25}x_{2}^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{25}x_{2}^{0}$$

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

$$\frac{3}{25}\times 1$$

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

$$\frac{3}{25}$$