compute the derivative of the given function.\n$k(x)=\\cos^{-1}(6x)$
compute the derivative of the given function.\n$k(x)=\\cos^{-1}(6x)$
Answer
Explanation:
Step1: Recall the derivative formula for inverse cosine function
The derivative of (y = \cos^{-1}(u)) is (y^\prime=-\frac{1}{\sqrt{1 - u^{2}}}\cdot u^\prime) (by the chain - rule). Here (u = 6x), and (u^\prime=\frac{d}{dx}(6x)=6).
Step2: Substitute (u) and (u^\prime) into the formula
Substitute (u = 6x) and (u^\prime=6) into the formula (k^\prime(x)=-\frac{1}{\sqrt{1-(6x)^{2}}}\cdot6).
Answer:
(k^\prime(x)=-\frac{6}{\sqrt{1 - 36x^{2}}})