Solve x*6/5*1/10

$$x \times \frac{ 6 }{ 5 } \times \frac{ 1 }{ 10 }$$

Evaluate

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

Solution Steps

Multiply \frac{6}{5} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$x\times \frac{6\times 1}{5\times 10}$$

Do the multiplications in the fraction \frac{6\times 1}{5\times 10}.

$$x\times \frac{6}{50}$$

Reduce the fraction \frac{6}{50} to lowest terms by extracting and canceling out 2.

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

Differentiate w.r.t. x

$$\frac{3}{25} = 0.12$$

Steps Using Definition of a Derivative

Multiply \frac{6}{5} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{6\times 1}{5\times 10})$$

Do the multiplications in the fraction \frac{6\times 1}{5\times 10}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{6}{50})$$

Reduce the fraction \frac{6}{50} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{3}{25})$$

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

$$\frac{3}{25}x^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{25}x^{0}$$

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.

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