How to find F''(x)

[sand agate]

How to find F''(x)

[onyx jacinth]

$$F'(x) = f(x)$$

[queen meteor]

King Leo

[onyx jacinth]

You need not integrate

Now all you care about is $$\dv{x} \qty(\int_1^{x^2} \frac{\sqrt{8 + u^4}}{u} \dd{u})$$

[queen meteor]

King Leo

[onyx jacinth]

Notice how i changed the bounds of integration from t^2 to x^2

It becomes x^2

When i plug in t = x into f(t), i change all instances of t to x

✅

Do you know how to calculate the derivative of an integral?

You do not need to find the antiderivative

$$\dv{x} \qty(\int_{g(x)}^{h(x)} f(x) \dd{x} )= f(h(x)) \cdot \dv{h}{x} - f(g(x)) \cdot \dv{g}{x}$$

[queen meteor]

King Leo

[onyx jacinth]

This might look very complicated. But try to use this, and youll see its very easy to use

✅

Assuming right side is the subtraction, yes