What is the derivative of arccos(7x^3) ?

The derivative of arccos(7x^3) is -(21x^2)/(sqrt(1-49x^6))

What is the first derivative of arccos(7x^3) ?

The first derivative of arccos(7x^3) is -(21x^2)/(sqrt(1-49x^6))

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derivative of

arccos (7 x^{3})

- \frac{21 x ^{2}}{1 - 49 x ^{6}}

Solution steps

\frac{d}{d x} (arccos (7 x^{3}))

Apply the chain rule:

- \frac{1}{1 - ( 7 x ^{3} ) ^{2}} \frac{d}{d x} (7 x^{3})

= - \frac{1}{1 - ( 7 x ^{3} ) ^{2}} \frac{d}{d x} (7 x^{3})

\frac{d}{d x} (7 x^{3}) = 21 x^{2}

= - \frac{1}{1 - ( 7 x ^{3} ) ^{2}} \cdot 21 x^{2}

Simplify

- \frac{1}{1 - ( 7 x ^{3} ) ^{2}} \cdot 21 x^{2} : - \frac{21 x ^{2}}{1 - 49 x ^{6}}

= - \frac{21 x ^{2}}{1 - 49 x ^{6}}

What is the derivative of arccos(7x^3) ?
The derivative of arccos(7x^3) is -(21x^2)/(sqrt(1-49x^6))
What is the first derivative of arccos(7x^3) ?
The first derivative of arccos(7x^3) is -(21x^2)/(sqrt(1-49x^6))