What is the derivative of 1/(sqrt(1-sin^2(x))) ?

The derivative of 1/(sqrt(1-sin^2(x))) is sec(x)tan(x)

What is the first derivative of 1/(sqrt(1-sin^2(x))) ?

The first derivative of 1/(sqrt(1-sin^2(x))) is sec(x)tan(x)

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\frac{d}{d x} \frac{1}{1 - sin ^{2} ( x )}

sec (x) tan (x)

Solution steps

\frac{d}{d x} \frac{1}{1 - sin ^{2} ( x )}

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= sec (x) tan (x)

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