Solve 8*10^7/pi(5)(193)(115)E*1-100^2/2(115)^2

$$\frac { 8 \times 10 ^ { 7 } } { \pi ( 5 ) ( 193 ) ( 115 ) } E \times 1 \frac { - 100 ^ { 2 } } { 2 ( 115 ) ^ { 2 } }$$

Evaluate

$$-\frac{640000000E}{2348231\pi }$$

Solution Steps

Calculate 10 to the power of 7 and get 10000000.

$$\frac{8\times 10000000}{\pi \times 5\times 193\times 115}E\times 1\times \frac{-100^{2}}{2\times 115^{2}}$$

Multiply 8 and 10000000 to get 80000000.

$$\frac{80000000}{\pi \times 5\times 193\times 115}E\times 1\times \frac{-100^{2}}{2\times 115^{2}}$$

Multiply 5 and 193 to get 965.

$$\frac{80000000}{\pi \times 965\times 115}E\times 1\times \frac{-100^{2}}{2\times 115^{2}}$$

Multiply 965 and 115 to get 110975.

$$\frac{80000000}{\pi \times 110975}E\times 1\times \frac{-100^{2}}{2\times 115^{2}}$$

Calculate 100 to the power of 2 and get 10000.

$$\frac{80000000}{\pi \times 110975}E\times 1\times \frac{-10000}{2\times 115^{2}}$$

Calculate 115 to the power of 2 and get 13225.

$$\frac{80000000}{\pi \times 110975}E\times 1\times \frac{-10000}{2\times 13225}$$

Multiply 2 and 13225 to get 26450.

$$\frac{80000000}{\pi \times 110975}E\times 1\times \frac{-10000}{26450}$$

Reduce the fraction \frac{-10000}{26450} to lowest terms by extracting and canceling out 50.

$$\frac{80000000}{\pi \times 110975}E\times 1\left(-\frac{200}{529}\right)$$

Multiply 1 and -\frac{200}{529} to get -\frac{200}{529}.

$$\frac{80000000}{\pi \times 110975}E\left(-\frac{200}{529}\right)$$

Express \frac{80000000}{\pi \times 110975}E as a single fraction.

$$\frac{80000000E}{\pi \times 110975}\left(-\frac{200}{529}\right)$$

Cancel out 25 in both numerator and denominator.

$$\frac{3200000E}{4439\pi }\left(-\frac{200}{529}\right)$$

Multiply \frac{3200000E}{4439\pi } times -\frac{200}{529} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3200000E\times 200}{4439\pi \times 529}$$

Multiply -3200000 and 200 to get -640000000.

$$\frac{-640000000E}{4439\pi \times 529}$$

Multiply 4439 and 529 to get 2348231.

$$\frac{-640000000E}{2348231\pi }$$

Differentiate w.r.t. E

$$-\frac{640000000}{2348231 \pi} = -86.75395527851649$$