Solve 0.3*1/36*x

$$0.3 \times \frac { 1 } { 36 } \times x$$

Evaluate

$$\frac{x}{120}$$

Solution Steps

Convert decimal number 0.3 to fraction \frac{3}{10}.

$$\frac{3}{10}\times \frac{1}{36}x$$

Multiply \frac{3}{10} times \frac{1}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 1}{10\times 36}x$$

Do the multiplications in the fraction \frac{3\times 1}{10\times 36}.

$$\frac{3}{360}x$$

Reduce the fraction \frac{3}{360} to lowest terms by extracting and canceling out 3.

$$\frac{1}{120}x$$

Differentiate w.r.t. x

$$\frac{1}{120} = 0.008333333333333333$$

Steps Using Definition of a Derivative

Convert decimal number 0.3 to fraction \frac{3}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{10}\times \frac{1}{36}x)$$

Multiply \frac{3}{10} times \frac{1}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 1}{10\times 36}x)$$

Do the multiplications in the fraction \frac{3\times 1}{10\times 36}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{360}x)$$

Reduce the fraction \frac{3}{360} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{120}x)$$

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

$$\frac{1}{120}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{120}x^{0}$$

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

$$\frac{1}{120}\times 1$$

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

$$\frac{1}{120}$$