
Find the derivative of f*f* if f(x)=x50*f*(*x*)=*x*50.

It seems like there was a formatting issue in your question. Let me clarify what I think you are asking:

You want to find the derivative of a function \( f(x) = x^{50} \times g(x) \), where \( g(x) = x^{50} \) as well. So effectively, you're looking for the derivative of the product of two identical functions, \( f(x) = x^{50} \times x^{50} \).

Let's go through the steps:

### Step 1: Simplify the Function
First, simplify the function:
\[
f(x) = x^{50} \times x^{50} = x^{100}
\]

### Step 2: Differentiate Using the Power Rule
Now, differentiate \( f(x) = x^{100} \) using the power rule:
\[
f'(x) = 100 \cdot x^{100-1} = 100 \cdot x^{99}
\]

So, the derivative of \( f(x) = x^{100} \) is \( f'(x) = 100x^{99} \).

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How would you differentiate \( f(x) = x^{a} \times x^{b} \) where \( a \) and \( b \) are different?
2. What is the derivative of \( f(x) = (x^n)^m \) for general \( n \) and \( m \)?
3. How do you differentiate a product of functions using the product rule?
4. What happens when you differentiate \( f(x) = \frac{1}{x^{50}} \times x^{50} \)?
5. Can you find the second derivative of \( f(x) = x^{100} \)?

**Tip:** When simplifying before differentiating, always look for ways to reduce the expression to its simplest form, as it can make the differentiation process much easier.

Learn how to find the derivative of the function f(x) = x^50 * x^50 using the power rule for differentiation. This problem involves differentiating a product of two identical functions and simplifying the expression. Suitable for advanced high school students or those studying calculus.

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