The image contains a mathematical expression, but due to the resolution, it's not completely clear. However, I can decipher a part of it, and it seems like you are dealing with a logarithmic equation involving a partial derivative.

The expression seems to resemble: $\frac{\partial}{\partial t} \log \left( y^{\text{something}} \right) = \text{some equation involving fractions and derivatives}.$

To help you better, I suggest either uploading a clearer image or you could type out the equation, and I can assist with the detailed solution.

Would you like to try that or re-upload the image?

Additionally, here are some relevant questions:

1. Are you working with logarithmic differentiation in this problem?
2. Is the equation related to partial differential equations (PDE)?
3. Is the context of the problem based on a physical or mathematical model?
4. Are you looking for a specific solution or just a general explanation?
5. Does the problem involve functions with multiple variables?

Tip: When working with partial derivatives, it's important to identify which variables are being held constant, as this can significantly affect the outcome of the derivative.