Solve =x/24*4/14

$$= \frac { x } { 24 } \cdot \frac { 4 } { 14 }$$

Evaluate

$$\frac{x}{84}$$

Solution Steps

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

$$\frac{x}{24}\times \frac{2}{7}$$

Multiply \frac{x}{24} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\times 2}{24\times 7}$$

Cancel out 2 in both numerator and denominator.

$$\frac{x}{7\times 12}$$

Multiply 7 and 12 to get 84.

$$\frac{x}{84}$$

Differentiate w.r.t. x

$$\frac{1}{84} = 0.011904761904761904$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{24}\times \frac{2}{7})$$

Multiply \frac{x}{24} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times 2}{24\times 7})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{7\times 12})$$

Multiply 7 and 12 to get 84.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{84})$$

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

$$\frac{1}{84}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{84}x^{0}$$

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

$$\frac{1}{84}\times 1$$

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

$$\frac{1}{84}$$