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Step-by-step Solution

Derive the function $\arctan\left(\sqrt{x}\right)$ with respect to x

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Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\arctan\left(\sqrt{x}\right)\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{\frac{d}{dx}\left(\sqrt{x}\right)}{1+\left(\sqrt{x}\right)^2}$

Unlock this full step-by-step solution!

Learn how to solve differential calculus problems step by step online. Derive the function arctan(x^0.5) with respect to x. Taking the derivative of arctangent. Cancel exponents \frac{1}{2} and 2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.

Answer

$\frac{\frac{1}{2}}{\sqrt{x}\left(1+x\right)}$

Problem Analysis

$\frac{d}{dx}\left(\arctan\left(\sqrt{x}\right)\right)$

Main topic:

Differential calculus

Related formulas:

2. See formulas

Time to solve it:

~ 0.05 seconds