What is (\partial)/(\partial x)(1/(cos^2(x))) ?

The answer to (\partial)/(\partial x)(1/(cos^2(x))) is 2sec^2(x)tan(x)

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(\partial)/(\partial x)(1/(cos^2(x)))

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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)

\int x 3 x^{2} - 1 d x

\frac{1}{( s ^{2} - 9 )}

\frac{d y}{d x} + 2 x^{2} y = 11 x^{2}

\int \frac{e ^{2 x} + 1}{e ^{2 x} - 1} d x

What is (\partial)/(\partial x)(1/(cos^2(x))) ?
The answer to (\partial)/(\partial x)(1/(cos^2(x))) is 2sec^2(x)tan(x)