If y=1/√x then dy/dx is equal to?

Question

Answer

Derivative of y=1/√x

To find the derivative of y=1/√x, we can use the power rule of differentiation.

Power Rule

The power rule states that if y=x^n, then dy/dx=nx^(n-1).

Using the Power Rule

We can rewrite y=1/√x as y=x^(-1/2). Using the power rule of differentiation, we get:

dy/dx = (-1/2)x^(-1/2-1)

Simplifying the exponent, we get:

dy/dx = (-1/2)x^(-3/2)

Simplifying the Expression

Now, we can simplify the expression by multiplying the numerator and denominator by √x:

dy/dx = (-1/2)x^(-3/2) * √x/√x

Simplifying the expression further, we get:

dy/dx = (-1/2)√x/x

Therefore, the derivative of y=1/√x is dy/dx = (-1/2)√x/x.

Conclusion

The derivative of y=1/√x is dy/dx = (-1/2)√x/x. This can be found using the power rule of differentiation and simplifying the expression.

Answer

-1/2x√x