Solve 2375698/x^4+376^6/frac{97{27.339^4}}

$$\frac { \frac { 2375698 } { x ^ { 4 } + 376 ^ { 6 } } } { \frac { 97 } { 27.339 ^ { 4 } } }$$

Evaluate

$$\frac{663577629037398608583609}{48500000000000\left(x^{4}+2825706623205376\right)}$$

Solution Steps

Divide \frac{2375698}{x^{4}+376^{6}} by \frac{97}{27.339^{4}} by multiplying \frac{2375698}{x^{4}+376^{6}} by the reciprocal of \frac{97}{27.339^{4}}.

$$\frac{2375698\times 27.339^{4}}{\left(x^{4}+376^{6}\right)\times 97}$$

Calculate 27.339 to the power of 4 and get 558638.033148488241.

$$\frac{2375698\times 558638.033148488241}{\left(x^{4}+376^{6}\right)\times 97}$$

Multiply 2375698 and 558638.033148488241 to get 1327155258074.797217167218.

$$\frac{1327155258074.797217167218}{\left(x^{4}+376^{6}\right)\times 97}$$

Calculate 376 to the power of 6 and get 2825706623205376.

$$\frac{1327155258074.797217167218}{\left(x^{4}+2825706623205376\right)\times 97}$$

Use the distributive property to multiply x^{4}+2825706623205376 by 97.

$$\frac{1327155258074.797217167218}{97x^{4}+274093542450921472}$$

Differentiate w.r.t. x

$$-\frac{663577629037398608583609x^{3}}{12125000000000\left(x^{4}+2825706623205376\right)^{2}}$$