Question

Differentiate

`√(x) + (1)/(5x) - 3`
with respect to their variable ​

Answer 1

`\\ \tt\longmapsto (d)/(dx)√(x)+(1)/(5x)-3`

`\\ \tt\longmapsto (d)/(dx)x^{(1)/(2)}+5x^(-1)-3`

• Derivative of any constant is 0

`\\ \tt\longmapsto (d)/(dx)x^{(1)/(2)}+5x^(-1)`

`\boxed{\sf (d(x^n))/(dx)=nx^(n-1)}`

`\\ \tt\longmapsto (1)/(2)x^{(-1)/(2)}-5x^(-2)`

`\\ \tt\longmapsto (x)/(2)^{(-1)/(2)}-(1)/(5x^2)`

`\\ \tt\longmapsto -\sqrt{(x)/(2)}-(1)/(5x^2)`