The derivative of $\frac { \sqrt { x } } { x } - \sqrt { x ^ { 2 } + 3 }$ is $- \frac { 1 } { 2 } x ^ { - \frac { 3 } { 2 } } - \frac { 1 } { 2 } \left( x ^ { 2 } + 3 \right) ^ { - \frac { 1 } { 2 } }$ .

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The derivative of $\frac { \sqrt { x } } { x } - \sqrt { x ^ { 2 } + 3 }$ simplifies to $- \frac { 1 } { 2 } x ^ { - \frac { 3 } { 2 } } - \frac { x } { \sqrt { x ^ { 2 } + 3 } }$, because the derivative of $\frac { \sqrt { x } } { x }$ is $- \frac { 1 } { 2 } x ^ { - \frac { 3 } { 2 } }$ and the derivative of $- \sqrt { x ^ { 2 } + 3 }$ is $- \frac { x } { \sqrt { x ^ { 2 } + 3 } }$ using the chain rule.

The Derivative Of xx−x2+3\frac { \sqrt { x } } { x } - \sqrt { x ^ { 2 } + 3 }xx​​−x2+3​

The Derivative Of $\frac { \sqrt { x } } { x } - \sqrt { x ^ { 2 } + 3 }$