if ( y = sin^{-1}(5x) ), then ( \frac{dy}{dx} = )
if ( y = sin^{-1}(5x) ), then ( \frac{dy}{dx} = )
Answer
Explanation:
Step1: Apply the chain rule
Let (u = 5x), then (y=\sin^{-1}(u)). The derivative of (\sin^{-1}(u)) with respect to (u) is (\frac{1}{\sqrt{1 - u^{2}}}), and the derivative of (u = 5x) with respect to (x) is (5).
Step2: Combine using the chain rule formula (\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx})
(\frac{dy}{dx}=\frac{1}{\sqrt{1-(5x)^{2}}}\cdot5)
Answer:
(\frac{5}{\sqrt{1 - 25x^{2}}})