by Marco Gleason
Published 2 years ago
Updated 2 years ago
The derivative of root x is given by d(√x)/dx = (1/2) x-1/2 or 1/(2√x). Root x given by √x is an exponential function with x as the variable and base as 1/2. We can calculate the derivative of root x using the Power Rule and First Principle of Derivatives.
Derivative of square root of x from first principle
Let $f (x)=\sqrt {x}.$ We need to find the derivative of $f (x).$ From first principle of derivatives, we have
Application of Derivative of square root of x
Using this fact, we can find the derivatives of many functions involving square roots using the chain rule of derivatives. The derivative of the square root of 3x+2 will be calculated as follows:
Recommend this Website
If you like this website, then please support it by giving it a Like. Thank you!
Book Recommendation
An extremely well-written book for students taking Calculus for the first time as well as those who need a refresher. This book makes you realize that Calculus isn't that tough after all. → to the book
Result
Above, enter the function to derive. Differentiation variable and more can be changed in " Options ". Click " Go! " to start the derivative calculation. The result will be shown further below.
How the Derivative Calculator Works
For those with a technical background, the following section explains how the Derivative Calculator works.
How to find derivative of square root?
To find the derivative of a square root function, you need to remember that the square root of any number or variable can also be written as an exponent. The term below the square root (radical) sign is written as the base, and it is raised to the exponent of 1/2.
How to write the denominator of a derivative?
Write the denominator as double the original square root. Using this shortcut, the denominator will be two times the original square root function. Thus, for the three sample functions above, the denominators of the derivatives will be:
What rule is used to find derivatives?
Review the power rule for derivatives. The first rule you probably learned for finding derivatives is the power rule . This rule says that for a variable
What does it mean to have a negative exponent?
At this stage, you need to recognize that a negative exponent means to take the reciprocal of what the number would be with the positive exponent. The exponent of
1 hours ago
y = 2 x 2 + 5. Differentiating with respect to variable x, we get. d y d x = d d x 2 x 2 + 5. Now using the formula derivative of a square root, we have. d y d x = 1 2 2 x 2 + 5 d d x ( 2 x 2 + 5) d y d x = …
15 hours ago
· Derivative of Root x by Logarithmic Differentiation. Now, we will find the derivative of √x with the help of the logarithmic derivative. Write. y= √x. ⇒ y = x 1/2. Taking natural …
2 hours ago
The Derivative Calculator lets you calculate derivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. It helps you practice by …
4.How to find the derivative of square root of x (steps)
Url:https://www.youtube.com/watch?v=hddQ_bYpAOg
4 hours ago
· This rule says that for a variable raised to any exponent , the derivative is as follows: [1] f ( x) = x a {\displaystyle f (x)=x^ {a}} f ′ ( x) = a x a − 1 {\displaystyle f^ {\prime } …
18 hours ago
To take the derivative of the square root of x, we first convert the square root of x to an exponent. So we can transform $\sqrt{x}=x^{\frac{1}{2}}$ Now we can go solution step by step:
13 hours ago
Enter the function you want to find the derivative of in the editor. The Derivative Calculator supports solving first, second...., fourth derivatives, as well as implicit differentiation and …
26 hours ago
Find the Derivative - d/dx f (x) = fifth root of x. f (x) = 5√x f ( x) = x 5. Use n√ax = ax n a x n = a x n to rewrite 5√x x 5 as x1 5 x 1 5. d dx [x1 5] d d x [ x 1 5] Differentiate using the Power Rule which …
