Solve y:10^3/10^9

$$y : \frac { 10 ^ { 3 } } { 10 ^ { 9 } }$$

Evaluate

$$1000000y$$

Solution Steps

Rewrite 10^{9} as 10^{3}\times 10^{6}. Cancel out 10^{3} in both numerator and denominator.

$$\frac{y}{\frac{1}{10^{6}}}$$

Divide y by \frac{1}{10^{6}} by multiplying y by the reciprocal of \frac{1}{10^{6}}.

$$y\times 10^{6}$$

Calculate 10 to the power of 6 and get 1000000.

$$y\times 1000000$$

Differentiate w.r.t. y

$$1000000$$

Steps Using Definition of a Derivative

Rewrite 10^{9} as 10^{3}\times 10^{6}. Cancel out 10^{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y}{\frac{1}{10^{6}}})$$

Divide y by \frac{1}{10^{6}} by multiplying y by the reciprocal of \frac{1}{10^{6}}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y\times 10^{6})$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y\times 1000000)$$

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

$$1000000y^{1-1}$$

Subtract 1 from 1.

$$1000000y^{0}$$

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

$$1000000\times 1$$

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

$$1000000$$