Solve 4*2/5*2*75*y

$$\frac { 4 \times 2 } { 5 \times 2 } \times 75 \times y$$

Evaluate

$$60y$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{2\times 2}{5}\times 75y$$

Multiply 2 and 2 to get 4.

$$\frac{4}{5}\times 75y$$

Express \frac{4}{5}\times 75 as a single fraction.

$$\frac{4\times 75}{5}y$$

Multiply 4 and 75 to get 300.

$$\frac{300}{5}y$$

Divide 300 by 5 to get 60.

$$60y$$

Differentiate w.r.t. y

$$60$$

Steps Using Definition of a Derivative

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2\times 2}{5}\times 75y)$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{4}{5}\times 75y)$$

Express \frac{4}{5}\times 75 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{4\times 75}{5}y)$$

Multiply 4 and 75 to get 300.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{300}{5}y)$$

Divide 300 by 5 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}y}(60y)$$

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

$$60y^{1-1}$$

Subtract 1 from 1.

$$60y^{0}$$

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

$$60\times 1$$

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

$$60$$