What is the derivative of sin(arccos(3x)) ?

The derivative of sin(arccos(3x)) is -(9x)/(sqrt(1-9x^2))

What is the first derivative of sin(arccos(3x)) ?

The first derivative of sin(arccos(3x)) is -(9x)/(sqrt(1-9x^2))

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\frac{d}{d x} (sin (arccos (3 x)))

- \frac{9 x}{1 - 9 x ^{2}}

Solution steps

\frac{d}{d x} (sin (arccos (3 x)))

Simplify

sin (arccos (3 x)) : 1 - 9 x^{2}

= \frac{d}{d x} (1 - 9 x^{2})

Apply the chain rule:

\frac{1}{2 1 - 9 x ^{2}} \frac{d}{d x} (1 - 9 x^{2})

= \frac{1}{2 1 - 9 x ^{2}} \frac{d}{d x} (1 - 9 x^{2})

\frac{d}{d x} (1 - 9 x^{2}) = - 18 x

= \frac{1}{2 1 - 9 x ^{2}} (- 18 x)

Simplify

\frac{1}{2 1 - 9 x ^{2}} (- 18 x) : - \frac{9 x}{1 - 9 x ^{2}}

= - \frac{9 x}{1 - 9 x ^{2}}

x \to 3 - lim (3 - x)

y^{^{''}} + 2 y^{^{'}} = 1, y (0) = 1, y^{^{'}} (0) = 0

\int_{0}^{2} 4 d x

\int (e^{x} + e^{- x})^{2} d x

\int_{0}^{\frac{π}{3}} 6 sec^{3} (x) d x

What is the derivative of sin(arccos(3x)) ?
The derivative of sin(arccos(3x)) is -(9x)/(sqrt(1-9x^2))
What is the first derivative of sin(arccos(3x)) ?
The first derivative of sin(arccos(3x)) is -(9x)/(sqrt(1-9x^2))