Question

Find the derivative of y=√x​

Answer 1

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Since the square root of x is the second root of x, it is equal to x raised to the power of 1/2. You may be wondering why we want to think of the square root of x in this way. Well, as it turns out, we have a nice formula we can use to find the derivative of xa.

⚫How do you differentiate square root of x?

➡️To differentiate the square root of x using the power rule, rewrite the square root as an exponent, or raise x to the power of 1/2. Find the derivative with the power rule, which says that the inverse function of x is equal to 1/2 times x to the power of a-1, where a is the original exponent.

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Answer 2

Answer:

Concept:

       Geometrically, the slope of a function's graph or, more accurately, the slope of the tangent line at a point can be used to understand the derivative of a function. Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.

       Differentiation is the process of determining a derivative, which is one of the fundamental ideas of calculus. With an exponent of "n," the derivative formula is defined for the variable "x". A rational fraction or an integer can serve as the exponent "n."

Hence, the formula to calculate the derivative is:

$\frac{d}{dx}$ ×$x^{n}$=n.$x^{n-1}$

Step-by-step explanation:

Given:

The equation y=√x.

To find:

The derivative of y=√x.

Solution:

Let us differentiate ,

y=√x

$y=x^{\frac{1}{2} }$

$\frac{dy}{dx} =\frac{d}{dx} x^{\frac{1}{2 }$

    =  $\frac{1}{2} x^{\frac{1}{2}-1 }$

    =  $\frac{1}{2} x^{\frac{-1}{2 }$

    =  $\frac{1}{2x^{\frac{1}{2} } }$

    =   $\frac{1}{2\sqrt{x} }$

Hence the derivative of y=√x is   $\frac{1}{2\sqrt{x} }$.

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