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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$
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$\frac{d}{dx}\left(x^2\right)2^x\ln\left(2x\right)+x^2\left(\frac{d}{dx}\left(2^x\right)\ln\left(2x\right)+2^x\frac{d}{dx}\left(\ln\left(2x\right)\right)\right)$
Learn how to solve problems step by step online. Find the derivative of x^22^xln(2x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The product of powers of the same base is equal to the base raised to the sum of the exponents: a^m\cdot a^n=a^{m+n}. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.