What is the derivative of (1+arccos(3x)^3) ?

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

What is the first derivative of (1+arccos(3x)^3) ?

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

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\frac{d}{d x} ((1 + arccos (3 x))^{3})

- \frac{9 ( 1 + arccos ( 3 x ) ) ^{2}}{- 9 x ^{2} + 1}

Solution steps

\frac{d}{d x} ((1 + arccos (3 x))^{3})

Apply the chain rule:

3 (1 + arccos (3 x))^{2} \frac{d}{d x} (1 + arccos (3 x))

= 3 (1 + arccos (3 x))^{2} \frac{d}{d x} (1 + arccos (3 x))

\frac{d}{d x} (1 + arccos (3 x)) = - \frac{3}{- 9 x ^{2} + 1}

= 3 (1 + arccos (3 x))^{2} (- \frac{3}{- 9 x ^{2} + 1})

Simplify

3 (1 + arccos (3 x))^{2} (- \frac{3}{- 9 x ^{2} + 1}) : - \frac{9 ( 1 + arccos ( 3 x ) ) ^{2}}{- 9 x ^{2} + 1}

= - \frac{9 ( 1 + arccos ( 3 x ) ) ^{2}}{- 9 x ^{2} + 1}

\int ∣ 2 x ∣ d x

f (x) = 3 x^{5} e^{2 x}

x \to 0 lim (\frac{1}{x + 1} - 1)

e^{- 0.5} (2 x + 1)^{0.5}

\int cos^{3} (x s i) n^{5} x d x

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