Final answer to the problem
$8x^{7}\log_{2}\left(x\right)+\frac{x^{7}}{\ln\left(2\right)}$
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Step-by-step Solution
Learn how to solve product rule of differentiation problems step by step online. Find the derivative of x^8log2(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^8 and g=\log_{2}\left(x\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}. We can find the derivative of a logarithm of any base using the change of base formula. Before deriving, we must pass the logarithm to base e: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. The derivative of a function multiplied by a constant (\frac{1}{\ln\left(2\right)}) is equal to the constant times the derivative of the function.
Final answer to the problem
$8x^{7}\log_{2}\left(x\right)+\frac{x^{7}}{\ln\left(2\right)}$
