Final answer:
To find dy/dx where y=log₂(x²+1), we can use the chain rule of differentiation by finding dy/du and du/dx. Then, we combine the results to get dy/dx.
Step-by-step explanation:
To find dy/dx where y=log₂(x²+1), we can use the chain rule of differentiation. Let's break down the steps:
- Firstly, let u=x²+1
- Next, find dy/du by differentiating log₂(u), which gives 1/(u*ln(2))
- Finally, find du/dx by differentiating u=x²+1, which gives 2x
Therefore, combining the results, we have:
dy/dx = dy/du * du/dx = 1/(u*ln(2)) * 2x = 2x/(u*ln(2))
To find the derivative dy/dx for y=log₂(x²+1), convert the base 2 logarithm to natural logarithm and then apply the chain rule to find the derivative.
The student has asked to find the derivative of y=log₂(x²+1). To find dy/dx, we will use the chain rule and the logarithmic differentiation principles. Given that the logarithm can be converted to natural logarithm using the formula log₂x = ln x / ln 2, we rewrite the function as y = ln(x²+1) / ln 2. The derivative of ln(x²+1) with respect to x is 2x / (x²+1), and after applying the chain rule, we divide by ln 2 to obtain the derivative with respect to the base 2 logarithm.