What is the derivative of y= 1/(cos^2(x)) ?

The derivative of y= 1/(cos^2(x)) is 2sec^2(x)tan(x)

What is the first derivative of y= 1/(cos^2(x)) ?

The first derivative of y= 1/(cos^2(x)) is 2sec^2(x)tan(x)

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derivative of

y = \frac{1}{cos ^{2} ( x )}

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

Solution steps

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

Simplify

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

s^{5}

\int \frac{1 + x}{x + 1} d x

\int (tan (x)) d x

\int \frac{1}{sin ^{2} ( y )} d y

\int 121 - x^{2} d x

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