Solve 6.626*10^-34Js*3*10^8ms^-1/0.24*10^-18J

$$\frac { 6.626 \times 10 ^ { - 34 } Js \times 3 \times 10 ^ { 8 } ms ^ { - 1 } } { 0.24 \times 10 ^ { - 18 } J }$$

Evaluate

$$\frac{3313m}{4000000000}$$

Solution Steps

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

$$\frac{6.626\times 10^{-26}Js\times 3ms^{-1}}{0.24\times 10^{-18}J}$$

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

$$\frac{6.626\times 10^{-26}J\times 3m}{0.24\times 10^{-18}J}$$

Cancel out J in both numerator and denominator.

$$\frac{3\times 6.626\times 10^{-26}m}{0.24\times 10^{-18}}$$

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

$$\frac{3\times 6.626m}{0.24\times 10^{8}}$$

Multiply 3 and 6.626 to get 19.878.

$$\frac{19.878m}{0.24\times 10^{8}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{19.878m}{0.24\times 100000000}$$

Multiply 0.24 and 100000000 to get 24000000.

$$\frac{19.878m}{24000000}$$

Divide 19.878m by 24000000 to get 0.00000082825m.

$$0.00000082825m$$

Differentiate w.r.t. m

$$0.00000082825$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{6.626\times 10^{-26}Js\times 3ms^{-1}}{0.24\times 10^{-18}J})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{6.626\times 10^{-26}J\times 3m}{0.24\times 10^{-18}J})$$

Cancel out J in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{3\times 6.626\times 10^{-26}m}{0.24\times 10^{-18}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{3\times 6.626m}{0.24\times 10^{8}})$$

Multiply 3 and 6.626 to get 19.878.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{19.878m}{0.24\times 10^{8}})$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{19.878m}{0.24\times 100000000})$$

Multiply 0.24 and 100000000 to get 24000000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{19.878m}{24000000})$$

Divide 19.878m by 24000000 to get 0.00000082825m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(0.00000082825m)$$

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

$$0.00000082825m^{1-1}$$

Subtract 1 from 1.

$$0.00000082825m^{0}$$

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

$$0.00000082825\times 1$$

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

$$0.00000082825$$