Solve 5/6x36/50

$$\frac { 5 } { 6 } x \frac { 36 } { 50 }$$

Evaluate

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

Solution Steps

Reduce the fraction \frac{36}{50} to lowest terms by extracting and canceling out 2.

$$\frac{5}{6}x\times \frac{18}{25}$$

Multiply \frac{5}{6} times \frac{18}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 18}{6\times 25}x$$

Do the multiplications in the fraction \frac{5\times 18}{6\times 25}.

$$\frac{90}{150}x$$

Reduce the fraction \frac{90}{150} to lowest terms by extracting and canceling out 30.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Reduce the fraction \frac{36}{50} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{6}x\times \frac{18}{25})$$

Multiply \frac{5}{6} times \frac{18}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 18}{6\times 25}x)$$

Do the multiplications in the fraction \frac{5\times 18}{6\times 25}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{90}{150}x)$$

Reduce the fraction \frac{90}{150} to lowest terms by extracting and canceling out 30.

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

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.

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