find the derivative of the function $h(w)$, below. it may be to your advantage to simplify before…

Explanation:

Step1: Recall product - rule

The product - rule states that if (y = u\cdot v), then (y'=u'v + uv'). Here, (u = 7w) and (v=\arcsin w).

Step2: Find the derivative of (u)

The derivative of (u = 7w) with respect to (w) is (u'=\frac{d}{dw}(7w)=7).

Step3: Find the derivative of (v)

The derivative of (v=\arcsin w) with respect to (w) is (v'=\frac{1}{\sqrt{1 - w^{2}}}).

Step4: Apply the product - rule

(h'(w)=u'v+uv'). Substitute (u = 7w), (u' = 7), (v=\arcsin w), and (v'=\frac{1}{\sqrt{1 - w^{2}}}) into the product - rule formula. (h'(w)=7\arcsin w+7w\cdot\frac{1}{\sqrt{1 - w^{2}}})

Answer:

(7\arcsin w+\frac{7w}{\sqrt{1 - w^{2}}})