Solve -0,2/6y3/-90

$$\frac { - 0,2 } { 6 } y \frac { 3 } { - 90 }$$

Evaluate

$$\frac{y}{900}$$

Solution Steps

Expand \frac{-0,2}{6} by multiplying both numerator and the denominator by 10.

$$\frac{-2}{60}y\times \frac{3}{-90}$$

Reduce the fraction \frac{-2}{60} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{30}y\times \frac{3}{-90}$$

Reduce the fraction \frac{3}{-90} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{30}y\left(-\frac{1}{30}\right)$$

Multiply -\frac{1}{30} times -\frac{1}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-1\right)}{30\times 30}y$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{30\times 30}.

$$\frac{1}{900}y$$

Differentiate w.r.t. y

$$\frac{1}{900} = 0.0011111111111111111$$

Steps Using Definition of a Derivative

Expand \frac{-0,2}{6} by multiplying both numerator and the denominator by 10.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-2}{60}y\times \frac{3}{-90})$$

Reduce the fraction \frac{-2}{60} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{1}{30}y\times \frac{3}{-90})$$

Reduce the fraction \frac{3}{-90} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{1}{30}y\left(-\frac{1}{30}\right))$$

Multiply -\frac{1}{30} times -\frac{1}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-\left(-1\right)}{30\times 30}y)$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{30\times 30}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{900}y)$$

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

$$\frac{1}{900}y^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{900}y^{0}$$

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

$$\frac{1}{900}\times 1$$

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

$$\frac{1}{900}$$