Differentiate the function $$ G(x)=3 x^{-7}+5 x^{-9}+5 $$

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Find the first order derivative with respect to $$ x $$ for $$ 3x^{-7}+5x^{-9}+5 $$.
Evaluate the derivative by following steps:
- step0: Evaluate the derivative:
  $$\frac{d}{dx}\left(3x^{-7}+5x^{-9}+5ight)$$
- step1: Use differentiation rules:
  $$\frac{d}{dx}\left(3x^{-7}ight)+\frac{d}{dx}\left(5x^{-9}ight)+\frac{d}{dx}\left(5ight)$$
- step2: Calculate:
  $$-21x^{-8}-45x^{-10}+0$$
- step3: Remove 0:
  $$-21x^{-8}-45x^{-10}$$
- step4: Simplify:
  $$-\frac{21}{x^{8}}-45x^{-10}$$
- step5: Simplify:
  $$-\frac{21}{x^{8}}-\frac{45}{x^{10}}$$
- step6: Reduce fractions to a common denominator:
  $$-\frac{21x^{2}}{x^{8}	imes x^{2}}-\frac{45}{x^{10}}$$
- step7: Multiply:
  $$-\frac{21x^{2}}{x^{10}}-\frac{45}{x^{10}}$$
- step8: Transform the expression:
  $$\frac{-21x^{2}-45}{x^{10}}$$
- step9: Rewrite the fraction:
  $$-\frac{21x^{2}+45}{x^{10}}$$
The derivative of the function $$ G(x) = 3x^{-7} + 5x^{-9} + 5 $$ with respect to $$ x $$ is $$ -\frac{21x^{2} + 45}{x^{10}} $$.
The derivative of $$ G(x) $$ is $$ -\frac{21x^{2} + 45}{x^{10}} $$.

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