Final Answer
Step-by-step Solution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^2$ and $g=\arctan\left(5x\right)$
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$\frac{d}{dx}\left(x^2\right)\arctan\left(5x\right)+x^2\frac{d}{dx}\left(\arctan\left(5x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of x^2arctan(5x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^2 and g=\arctan\left(5x\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. The power of a product is equal to the product of it's factors raised to the same power.