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Popular >

derivative of 1/((cos(x)^2))

Solution

\frac{d}{d x} (\frac{1}{( cos ( x ) ) ^{2}})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{( cos ( x ) ) ^{2}})

Simplify

\frac{1}{( cos ( x ) ) ^{2}} : sec^{2} (x)

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

Apply the chain rule:

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

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= 2 sec (x) sec (x) tan (x)

Simplify

2 sec (x) sec (x) tan (x) : 2 sec^{2} (x) tan (x)

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

Popular Examples

derivative of (1+e^{-x}^{-1})

\frac{d}{d x} ((1 + e^{- x})^{- 1})

derivative of y=x^{2x+5}derivative of

y = x^{2 x + 5}

(\partial)/(\partial x)(ln(9-x^2-y^2))

\frac{\partial}{\partial x} (ln (9 - x^{2} - y^{2}))

(\partial)/(\partial z)(z(y-yz)^4)

\frac{\partial}{\partial z} (z (y - yz)^{4})

integral from 0 to 5 of e^{-x}

\int_{0}^{5} e^{- x} d x

Frequently Asked Questions (FAQ)

What is the derivative of 1/((cos(x)^2)) ?
The derivative of 1/((cos(x)^2)) is 2sec^2(x)tan(x)
What is the first derivative of 1/((cos(x)^2)) ?
The first derivative of 1/((cos(x)^2)) is 2sec^2(x)tan(x)