Final Answer
Step-by-step Solution
Specify the solving method
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=10^x$ and $g=\log_{5}\left(x\right)$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(10^x\right)\log_{5}\left(x\right)+10^x\frac{d}{dx}\left(\log_{5}\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 10^xlog5(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=10^x and g=\log_{5}\left(x\right). Applying the derivative of the exponential function. The derivative of the linear function is equal to 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)}.