Derivative of asin(6x)

Answer

6−36⋅x2+1\frac{6}{\sqrt{-36 \cdot x^{2}+1}}
6*sqrt(-36*x^2+1)^(-1)

Derivative of asin(6x)

Rule Used
Chain Rule
Steps
  1. Identify a composite function in arcsin⁡(6⋅x)\arcsin(6 \cdot x): use the chain rule ddxf(g(x))\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.
  2. Differentiate the outer function, then multiply by the inner derivative.
  3. Final answer: 6⋅s6 \cdot sqrt(-36⋅x236 \cdot x^2+1)^(-1)

The derivative of asin(6*x) is 6*sqrt(-36*x^2+1)^(-1).

Instant step-by-step solution for asin(6x)

DerivativeTrigonometricAdvanced
Share this result
Share on X

Derivative of asin(6x) = 6*sqrt(-36*x^2+1)^(-1) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-asin6x

How to find the derivative of asin(6x)

To find the derivative of asin(6x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.

Practice More Problems

Derivative of 1/x
Solve d/dx 1/x
Derivative of 1/x^2
Solve d/dx 1/x^2
Derivative of 10^x
Solve d/dx 10^x
Derivative of 2^x
Solve d/dx 2^x
Derivative of Abs(x)
Solve d/dx Abs(x)
Derivative of acos(x)
Solve d/dx acos(x)
Derivative of asin(x)
Solve d/dx asin(x)
Derivative of atan(x)
Solve d/dx atan(x)
Derivative of x^(1/3)
Solve d/dx x^(1/3)
Derivative of cos(2x)
Solve d/dx cos(2x)

Frequently Asked Questions

What is the derivative of asin(6x)?▼
The derivative of asin(6x) is 6*sqrt(-36*x^2+1)^(-1).
How do you find the derivative of asin(6x)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 6*sqrt(-36*x^2+1)^(-1).
Why is the derivative of asin(6x) equal to 6*sqrt(-36*x^2+1)^(-1)?▼
Because differentiation measures how a function changes — applying the rules to asin(6x) yields 6*sqrt(-36*x^2+1)^(-1). See the full step-by-step breakdown above.

Support via PayPal

Support free development ❤️