The derivative of $\frac { e ^ { - x } } { 1 + x ^ { 7 } }$ is $\frac { - e ^ { - x } \left( 1 + 7 x ^ { 6 } + x ^ { 7 } \right) } { \left( 1 + x ^ { 7 } \right) ^ { 2 } }$ .

Question

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The derivative of $\frac { e ^ { - x } } { 1 + x ^ { 7 } }$ can be found using the quotient rule, which is $\frac{v(u') - u(v')}{v^2}$ where $u = e^{-x}$ and $v = 1 + x^7$. Applying the rule, $u' = -e^{-x}$ and $v' = 7x^6$, leading to the given derivative.

The Derivative Of e−x1+x7\frac { e ^ { - x } } { 1 + x ^ { 7 } }1+x7e−x​

The Derivative Of $\frac { e ^ { - x } } { 1 + x ^ { 7 } }$