How do I solve more advanced derivative problems?

How do I solve more advanced derivative problems?

To tackle advanced derivative problems, it's essential to understand the rules of differentiation, such as the product rule, quotient rule, and chain rule. Do you have a specific problem in mind?

Yes, can you help me differentiate the function f(x) = x^3 * sin(x)?

Sure! To differentiate f(x) = x^3 * sin(x), we use the product rule. The derivative is f'(x) = (3x^2 * sin(x)) + (x^3 * cos(x)). Would you like to see a step-by-step breakdown?

Yes, please! I want to understand each step.

Alright! First, we identify u = x^3 and v = sin(x). The product rule states that f'(x) = u'v + uv'. So, we find u' = 3x^2 and v' = cos(x). Plugging these into the formula gives us the final derivative.

That makes sense! Can you give me another example?

Of course! How about differentiating f(x) = e^x * ln(x)? It's another application of the product rule.