Question

find the derivative of the function. f(x) = (x⁴ + 7x² − 5)⁶ f(x) = resources

Explanation:

Step1: Apply chain rule

Let $u = x^4 + 7x^2 - 5$, so $F(x) = u^6$. Then $F'(x) = 6u^5 \cdot u'$.

Step2: Compute derivative of u

$u' = 4x^3 + 14x$.

Step3: Substitute back u

$F'(x) = 6(x^4 + 7x^2 - 5)^5(4x^3 + 14x)$.

Answer:

$6(x^4 + 7x^2 - 5)^5(4x^3 + 14x)$