Derivative of asin(9x)

Answer

\frac{9}{\sqrt{-81 \cdot x^{2}+1}}

Derivative of asin(9x)

Rule Used: Chain Rule
Steps: Identify a composite function in $\arcsin(9 \cdot x)$ : use the chain rule $\frac{d}{dx} f(g(x))$ = f'(g(x))·g'(x). The inner derivative is required because a stretch or shift of the input changes how fast the output moves.
Differentiate the outer function, then multiply by the inner derivative.
Final answer: $9 \cdot s$ qrt(- $81 \cdot x^2$ +1)^(-1)

The derivative of asin(9*x) is 9*sqrt(-81*x^2+1)^(-1).

Instant step-by-step solution for asin(9x)

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Derivative of asin(9x) = 9*sqrt(-81*x^2+1)^(-1) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-asin9x

How to find the derivative of asin(9x)

To find the derivative of asin(9x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.

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Frequently Asked Questions

What is the derivative of asin(9x)?▼

The derivative of asin(9x) is 9*sqrt(-81*x^2+1)^(-1).

How do you find the derivative of asin(9x)?▼

Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 9*sqrt(-81*x^2+1)^(-1).

Why is the derivative of asin(9x) equal to 9*sqrt(-81*x^2+1)^(-1)?▼

Because differentiation measures how a function changes — applying the rules to asin(9x) yields 9*sqrt(-81*x^2+1)^(-1). See the full step-by-step breakdown above.

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