Solve G6.674*10^-1170^27.3510^22/1.73^2

$$G6.674 \times { 10 }^{ -11 } \frac{ { 70 }^{ 2 } 7.35 { 10 }^{ 22 } }{ { 1.73 }^{ 2 } }$$

Evaluate

$$\frac{24274110000000000000G_{6}}{29929}$$

Solution Steps

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

$$G_{6}\times 0.674\times \frac{1}{100000000000}\times \frac{70^{2}\times 7.35\times 10^{22}}{1.73^{2}}$$

Multiply 0.674 and \frac{1}{100000000000} to get \frac{337}{50000000000000}.

$$G_{6}\times \frac{337}{50000000000000}\times \frac{70^{2}\times 7.35\times 10^{22}}{1.73^{2}}$$

Calculate 70 to the power of 2 and get 4900.

$$G_{6}\times \frac{337}{50000000000000}\times \frac{4900\times 7.35\times 10^{22}}{1.73^{2}}$$

Multiply 4900 and 7.35 to get 36015.

$$G_{6}\times \frac{337}{50000000000000}\times \frac{36015\times 10^{22}}{1.73^{2}}$$

Calculate 10 to the power of 22 and get 10000000000000000000000.

$$G_{6}\times \frac{337}{50000000000000}\times \frac{36015\times 10000000000000000000000}{1.73^{2}}$$

Multiply 36015 and 10000000000000000000000 to get 360150000000000000000000000.

$$G_{6}\times \frac{337}{50000000000000}\times \frac{360150000000000000000000000}{1.73^{2}}$$

Calculate 1.73 to the power of 2 and get 2.9929.

$$G_{6}\times \frac{337}{50000000000000}\times \frac{360150000000000000000000000}{2.9929}$$

Expand \frac{360150000000000000000000000}{2.9929} by multiplying both numerator and the denominator by 10000.

$$G_{6}\times \frac{337}{50000000000000}\times \frac{3601500000000000000000000000000}{29929}$$

Multiply \frac{337}{50000000000000} and \frac{3601500000000000000000000000000}{29929} to get \frac{24274110000000000000}{29929}.

$$G_{6}\times \frac{24274110000000000000}{29929}$$

Differentiate w.r.t. G_6

$$\frac{24274110000000000000}{29929} = 811056500384242\frac{21182}{29929} = 811056500384242.8$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}G_{6}}(G_{6}\times 0.674\times \frac{1}{100000000000}\times \frac{70^{2}\times 7.35\times 10^{22}}{1.73^{2}})$$

Multiply 0.674 and \frac{1}{100000000000} to get \frac{337}{50000000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6}}(G_{6}\times \frac{337}{50000000000000}\times \frac{70^{2}\times 7.35\times 10^{22}}{1.73^{2}})$$

Calculate 70 to the power of 2 and get 4900.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6}}(G_{6}\times \frac{337}{50000000000000}\times \frac{4900\times 7.35\times 10^{22}}{1.73^{2}})$$

Multiply 4900 and 7.35 to get 36015.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6}}(G_{6}\times \frac{337}{50000000000000}\times \frac{36015\times 10^{22}}{1.73^{2}})$$

Calculate 10 to the power of 22 and get 10000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6}}(G_{6}\times \frac{337}{50000000000000}\times \frac{36015\times 10000000000000000000000}{1.73^{2}})$$

Multiply 36015 and 10000000000000000000000 to get 360150000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6}}(G_{6}\times \frac{337}{50000000000000}\times \frac{360150000000000000000000000}{1.73^{2}})$$

Calculate 1.73 to the power of 2 and get 2.9929.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6}}(G_{6}\times \frac{337}{50000000000000}\times \frac{360150000000000000000000000}{2.9929})$$

Expand \frac{360150000000000000000000000}{2.9929} by multiplying both numerator and the denominator by 10000.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6}}(G_{6}\times \frac{337}{50000000000000}\times \frac{3601500000000000000000000000000}{29929})$$

Multiply \frac{337}{50000000000000} and \frac{3601500000000000000000000000000}{29929} to get \frac{24274110000000000000}{29929}.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6}}(G_{6}\times \frac{24274110000000000000}{29929})$$

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

$$\frac{24274110000000000000}{29929}G_{6}^{1-1}$$

Subtract 1 from 1.

$$\frac{24274110000000000000}{29929}G_{6}^{0}$$

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

$$\frac{24274110000000000000}{29929}\times 1$$

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

$$\frac{24274110000000000000}{29929}$$