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Step-by-step Solution

Find the derivative using the product rule $\frac{d}{dx}\left(x^3\arctan\left(x^2\right)\right)$

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Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(x^3\arctan\left(x^2\right)\right)$

Learn how to solve product rule of differentiation problems step by step online.

$\frac{d}{dx}\left(x^3\right)\arctan\left(x^2\right)+x^3\frac{d}{dx}\left(\arctan\left(x^2\right)\right)$

Unlock this full step-by-step solution!

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(x^3arctan(x^2)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^3 and g=\arctan\left(x^2\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Taking the derivative of arctangent. Applying the power of a power property.

Answer

$3x^{2}\arctan\left(x^2\right)+\frac{2x^{4}}{\left(x^2-\sqrt{2}x+1\right)\left(x^2+\sqrt{2}x+1\right)}$

Problem Analysis