Solve =(6*63*10^-34Js)*(3*10^8ms^-1)/(5*10^-19J)

$$= \frac { ( 6 \cdot 63 \times 10 ^ { - 34 } J s ) \times ( 3 \times 10 ^ { 8 } m s ^ { - 1 } ) } { ( 5 \times 10 ^ { - 19 } J ) }$$

Evaluate

$$\frac{567m}{25000000}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$\frac{6\times 63\times 10^{-26}Js\times 3ms^{-1}}{5\times 10^{-19}J}$$

Multiply s and s^{-1} to get 1.

$$\frac{6\times 63\times 10^{-26}J\times 3m}{5\times 10^{-19}J}$$

Cancel out J in both numerator and denominator.

$$\frac{3\times 6\times 63\times 10^{-26}m}{5\times 10^{-19}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{3\times 6\times 63m}{5\times 10^{7}}$$

Multiply 3 and 6 to get 18.

$$\frac{18\times 63m}{5\times 10^{7}}$$

Multiply 18 and 63 to get 1134.

$$\frac{1134m}{5\times 10^{7}}$$

Calculate 10 to the power of 7 and get 10000000.

$$\frac{1134m}{5\times 10000000}$$

Multiply 5 and 10000000 to get 50000000.

$$\frac{1134m}{50000000}$$

Divide 1134m by 50000000 to get \frac{567}{25000000}m.

$$\frac{567}{25000000}m$$

Differentiate w.r.t. m

$$\frac{567}{25000000} = 2.268 \times 10^{-5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{6\times 63\times 10^{-26}Js\times 3ms^{-1}}{5\times 10^{-19}J})$$

Multiply s and s^{-1} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{6\times 63\times 10^{-26}J\times 3m}{5\times 10^{-19}J})$$

Cancel out J in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{3\times 6\times 63\times 10^{-26}m}{5\times 10^{-19}})$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{3\times 6\times 63m}{5\times 10^{7}})$$

Multiply 3 and 6 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{18\times 63m}{5\times 10^{7}})$$

Multiply 18 and 63 to get 1134.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1134m}{5\times 10^{7}})$$

Calculate 10 to the power of 7 and get 10000000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1134m}{5\times 10000000})$$

Multiply 5 and 10000000 to get 50000000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1134m}{50000000})$$

Divide 1134m by 50000000 to get \frac{567}{25000000}m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{567}{25000000}m)$$

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

$$\frac{567}{25000000}m^{1-1}$$

Subtract 1 from 1.

$$\frac{567}{25000000}m^{0}$$

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

$$\frac{567}{25000000}\times 1$$

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

$$\frac{567}{25000000}$$