Question

find the derivative of the function $h(w)$, below. it may be to your advantage to simplify before differentiating.
$h(w)=7warcsin w$
$h(w)=$

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:

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