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Popular >

derivative of sec^2(x^3)

Solution

\frac{d}{d x} (sec^{2} (x^{3}))

Solution

6 x^{2} sec^{2} (x^{3}) tan (x^{3})

Solution steps

\frac{d}{d x} (sec^{2} (x^{3}))

Apply the chain rule:

2 sec (x^{3}) \frac{d}{d x} (sec (x^{3}))

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

\frac{d}{d x} (sec (x^{3})) = sec (x^{3}) tan (x^{3}) \cdot 3 x^{2}

= 2 sec (x^{3}) sec (x^{3}) tan (x^{3}) \cdot 3 x^{2}

Simplify

2 sec (x^{3}) sec (x^{3}) tan (x^{3}) \cdot 3 x^{2} : 6 x^{2} sec^{2} (x^{3}) tan (x^{3})

= 6 x^{2} sec^{2} (x^{3}) tan (x^{3})

Popular Examples

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x \to 2 lim (- x + 7)

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\int \frac{x ^{3}}{x ^{4} + 6} d x

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(dy}{dx}=\frac{2x+5y)/x

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Frequently Asked Questions (FAQ)

What is the derivative of sec^2(x^3) ?
The derivative of sec^2(x^3) is 6x^2sec^2(x^3)tan(x^3)
What is the first derivative of sec^2(x^3) ?
The first derivative of sec^2(x^3) is 6x^2sec^2(x^3)tan(x^3)