Question

What is the derivative of arcsin(6x)

Answer 1

To find the derivative of arcsin(6x), you can use the chain rule. The derivative is 6/(sqrt(1-(6x)^2)).

Step-by-step explanation:

To find the derivative of arcsin(6x), we can use the chain rule of differentiation. Let u = 6x, then the derivative of u with respect to x is 6. Now, we can find the derivative of arcsin(u) with respect to u, which is 1/sqrt(1-u^2). Applying the chain rule, the derivative of arcsin(6x) with respect to x is 6/(sqrt(1-(6x)^2)).

Answer 2

`\bf sin^(-1)(6x)\\\\ -----------------------------\\\\ \textit{using the chain-rule}\implies \cfrac{d}{dx}\left[ sin^(-1)(6x) \right]\implies \cfrac{1}{√(1-(6x)^2)}\cdot 6\\\\ \cfrac{6}{√(1-36x^2)}`