Solve 12/15x3/4

$$\frac{ 12 }{ 15 } x \frac{ 3 }{ 4 }$$

Evaluate

$$\frac{3x}{5}$$

Solution Steps

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}x\times \frac{3}{4}$$

Multiply \frac{4}{5} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 3}{5\times 4}x$$

Cancel out 4 in both numerator and denominator.

$$\frac{3}{5}x$$

Differentiate w.r.t. x

$$\frac{3}{5} = 0.6$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{5}x\times \frac{3}{4})$$

Multiply \frac{4}{5} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 3}{5\times 4}x)$$

Cancel out 4 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{5}x)$$

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

$$\frac{3}{5}x^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{5}x^{0}$$

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

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

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

$$\frac{3}{5}$$