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Popular >

derivative of arccos(4x^3)

Solution

\frac{d}{d x} (arccos (4 x^{3}))

Solution

- \frac{12 x ^{2}}{1 - 16 x ^{6}}

Solution steps

\frac{d}{d x} (arccos (4 x^{3}))

Apply the chain rule:

- \frac{1}{1 - ( 4 x ^{3} ) ^{2}} \frac{d}{d x} (4 x^{3})

= - \frac{1}{1 - ( 4 x ^{3} ) ^{2}} \frac{d}{d x} (4 x^{3})

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

= - \frac{1}{1 - ( 4 x ^{3} ) ^{2}} \cdot 12 x^{2}

Simplify

- \frac{1}{1 - ( 4 x ^{3} ) ^{2}} \cdot 12 x^{2} : - \frac{12 x ^{2}}{1 - 16 x ^{6}}

= - \frac{12 x ^{2}}{1 - 16 x ^{6}}

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Frequently Asked Questions (FAQ)

What is the derivative of arccos(4x^3) ?
The derivative of arccos(4x^3) is -(12x^2)/(sqrt(1-16x^6))
What is the first derivative of arccos(4x^3) ?
The first derivative of arccos(4x^3) is -(12x^2)/(sqrt(1-16x^6))