Find the derivative of the function. F(x) = (x^4 + 7x^2 − 7)^9

We should apply chain rule for this.

f'(x) = $\frac{d(x^4 + 7x^2 − 7)^9}{dx}$ = $\frac{d(x^4 + 7x^2 − 7)^9}{d(x^4 + 7x^2 − 7)} \times \frac{d(x^4 + 7x^2 − 7)}{dx}$

Now, we can use $\frac{dx^n}{dx}$ = nx^n-1

= 9(x⁴ + 7x² - 7)⁸ × $(\frac{dx^4}{dx}$ + $7\frac{dx^2}{dx}$ - $\frac{d7}{dx})$

= 9(x⁴ + 7x² - 7)⁸ × (4x³ + 14x - 0)

= 9(x⁴ + 7x² - 7)⁸ (4x³ + 14x)

This question is also based on chain rule. Highly recommend to practice that question too.