What is the derivative of 1/(sqrt(cos(x))) ?

The derivative of 1/(sqrt(cos(x))) is (sin(x))/(2cos^{3/2)(x)}

What is the first derivative of 1/(sqrt(cos(x))) ?

The first derivative of 1/(sqrt(cos(x))) is (sin(x))/(2cos^{3/2)(x)}

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

\frac{sin ( x )}{2 cos ^{\frac{3}{2}} ( x )}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

= - \frac{1}{2 ( cos ( x ) ) ^{\frac{3}{2}}} \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

= - \frac{1}{2 ( cos ( x ) ) ^{\frac{3}{2}}} (- sin (x))

Simplify

- \frac{1}{2 cos ^{\frac{3}{2}} ( x )} (- sin (x)) : \frac{sin ( x )}{2 cos ^{\frac{3}{2}} ( x )}

= \frac{sin ( x )}{2 cos ^{\frac{3}{2}} ( x )}

x \to 0 lim (x e^{x})

\frac{d}{d x} ((\frac{x - 5}{2 x + 1})^{3})

\frac{2 s}{2 s + 1}

\frac{d}{d x} (\frac{4}{x ^{3}} + 3 x)

6 cos (6 x)

What is the derivative of 1/(sqrt(cos(x))) ?
The derivative of 1/(sqrt(cos(x))) is (sin(x))/(2cos^{3/2)(x)}
What is the first derivative of 1/(sqrt(cos(x))) ?
The first derivative of 1/(sqrt(cos(x))) is (sin(x))/(2cos^{3/2)(x)}