Differentiate the function:

𝑓(𝑥)=−7𝑥^14−𝑥^4+2𝑥−(1/𝑥^4)

Answer: 𝑓′(𝑥)=

To differentiate the function:

\[
f(x) = -7x^{14} - x^4 + 2x - \frac{1}{x^4}
\]

we will apply the power rule to each term. The power rule states that:

\[
\frac{d}{dx}(x^n) = nx^{n-1}
\]

### Differentiation of each term:

1. \( \frac{d}{dx}(-7x^{14}) = -7 \cdot 14x^{13} = -98x^{13} \)
2. \( \frac{d}{dx}(-x^4) = -4x^{3} \)
3. \( \frac{d}{dx}(2x) = 2 \)
4. \( \frac{d}{dx}\left(-\frac{1}{x^4}\right) = -\frac{d}{dx}(x^{-4}) = -(-4x^{-5}) = 4x^{-5} \)

### Combining the results:

\[
f'(x) = -98x^{13} - 4x^3 + 2 + 4x^{-5}
\]

Thus, the derivative is:

\[
f'(x) = -98x^{13} - 4x^3 + 2 + \frac{4}{x^5}
\]

Would you like further details on this differentiation process or have any questions?

Here are 5 related questions:
1. How do you differentiate composite functions using the chain rule?
2. How do you apply the product rule in differentiation?
3. Can you explain implicit differentiation with an example?
4. What is the derivative of exponential functions like \(e^x\)?
5. How do you find higher-order derivatives?

**Tip:** Always simplify terms involving negative exponents after differentiating to make the result more readable!

Differentiate the function: f(x) = -7x^14 - x^4 + 2x - (1/x^4)

Learn how to differentiate the function f(x) = -7x^14 - x^4 + 2x - 1/x^4 using the power rule of differentiation. This step-by-step guide covers the application of calculus techniques suitable for high school students in Grades 11-12.

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