DERIVATIVE OF SQUARE ROOT OF X

Question :

Find the derivative of √x with respect to x.

or

Given y = √x, find dy/dx, where x > 0.

Solution :

y = √x

Write the square root as exponent 1/2.

y = x^1/2

Find the derivative on both sides with respect to x using power rule of derivative. That is, in x^1/2, bring the exponent 1/2 in front of x and subtract 1 from the exponent 1/2.

Therefore, the derivative √x is

Example 1 :

Find dy/dx, if y = √(mx), where m is a constant.

Solution :

Example 2 :

Find dy/dx, if y = √(5x).

Solution :

Example 3 :

Find dy/dx, if y = √(x³).

Solution :

Example 4 :

Find dy/dx, if y = √(x³ + 5x² - 6x - 5).

Solution :

Example 5 :

Find dy/dx, if y = √sinx.

Solution :

Example 5 :

Find dy/dx, if y = √cosx.

Solution :

Example 5 :

Find dy/dx, if y = √tanx.

Solution :

Example 5 :

Find dy/dx, if y = √lnx.

Solution :

Example 5 :

Find dy/dx, if y = √5.

Solution :

We know that 5 is a constant. So, √5 is also a constant. Since the derivative of a constant is zero, the derivative √5 is zero.

y = √5

dy/dx = 0

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