Solve 2*6,67*10^-11*3km/300000km/h

$$\frac { 2 \cdot 6,67 \cdot 10 ^ { - 11 } \cdot 3 k m } { 300000 k m / h }$$

Evaluate

$$\frac{667h}{500000000000000000}$$

Solution Steps

Multiply 2 and 6,67 to get 13,34.

$$\frac{13,34\times 10^{-11}\times 3km}{\frac{300000km}{h}}$$

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$\frac{13,34\times \frac{1}{100000000000}\times 3km}{\frac{300000km}{h}}$$

Multiply 13,34 and \frac{1}{100000000000} to get \frac{667}{5000000000000}.

$$\frac{\frac{667}{5000000000000}\times 3km}{\frac{300000km}{h}}$$

Multiply \frac{667}{5000000000000} and 3 to get \frac{2001}{5000000000000}.

$$\frac{\frac{2001}{5000000000000}km}{\frac{300000km}{h}}$$

Divide \frac{2001}{5000000000000}km by \frac{300000km}{h} by multiplying \frac{2001}{5000000000000}km by the reciprocal of \frac{300000km}{h}.

$$\frac{\frac{2001}{5000000000000}kmh}{300000km}$$

Cancel out km in both numerator and denominator.

$$\frac{\frac{2001}{5000000000000}h}{300000}$$

Divide \frac{2001}{5000000000000}h by 300000 to get \frac{667}{500000000000000000}h.

$$\frac{667}{500000000000000000}h$$

Differentiate w.r.t. h

$$0,000000000000001334$$

Steps Using Definition of a Derivative

Multiply 2 and 6,67 to get 13,34.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{13,34\times 10^{-11}\times 3km}{\frac{300000km}{h}})$$

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{13,34\times \frac{1}{100000000000}\times 3km}{\frac{300000km}{h}})$$

Multiply 13,34 and \frac{1}{100000000000} to get \frac{667}{5000000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{\frac{667}{5000000000000}\times 3km}{\frac{300000km}{h}})$$

Multiply \frac{667}{5000000000000} and 3 to get \frac{2001}{5000000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{\frac{2001}{5000000000000}km}{\frac{300000km}{h}})$$

Divide \frac{2001}{5000000000000}km by \frac{300000km}{h} by multiplying \frac{2001}{5000000000000}km by the reciprocal of \frac{300000km}{h}.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{\frac{2001}{5000000000000}kmh}{300000km})$$

Cancel out km in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{\frac{2001}{5000000000000}h}{300000})$$

Divide \frac{2001}{5000000000000}h by 300000 to get \frac{667}{500000000000000000}h.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{667}{500000000000000000}h)$$

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

$$\frac{667}{500000000000000000}h^{1-1}$$

Subtract 1 from 1.

$$\frac{667}{500000000000000000}h^{0}$$

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

$$\frac{667}{500000000000000000}\times 1$$

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

$$\frac{667}{500000000000000000}$$