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derivative of sqrt(sec(x^3))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

= \frac{1}{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}

= \frac{1}{2 sec ( x ^{3} )} sec (x^{3}) tan (x^{3}) \cdot 3 x^{2}

Simplify

\frac{1}{2 sec ( x ^{3} )} sec (x^{3}) tan (x^{3}) \cdot 3 x^{2} : \frac{3 x ^{2} tan ( x ^{3} ) sec ( x ^{3} )}{2}

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

Popular Examples

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\int_{4}^{\infty} x e^{- 2 x} d x

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\int_{- 3}^{5} 2 y - (y^{2} - 15) d y

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Frequently Asked Questions (FAQ)

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