Question

question: 5
show this question in the book
compute the derivative of the given function.
h(q)=sin(sin^{-1}(q))
submit randomize reset

Explanation:

Step1: Simplify the function

Since $\sin(\sin^{-1}(q)) = q$ for $q\in[- 1,1]$, so $h(q)=q$.

Step2: Differentiate the simplified function

The derivative of $y = x^n$ is $y^\prime=nx^{n - 1}$. For $h(q)=q = q^1$, using the power rule $n = 1$, then $h^\prime(q)=\frac{d}{dq}(q^1)=1\times q^{1-1}=1$.

Answer:

$1$