What is the derivative of 4/(sqrt(sec(x))) ?

The derivative of 4/(sqrt(sec(x))) is -2tan(x)cos^{1/2}(x)

What is the first derivative of 4/(sqrt(sec(x))) ?

The first derivative of 4/(sqrt(sec(x))) is -2tan(x)cos^{1/2}(x)

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\frac{d}{d x} (\frac{4}{sec ( x )})

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

Solution steps

\frac{d}{d x} (\frac{4}{sec ( x )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (\frac{1}{sec ( x )})

Apply exponent rule:

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

= 4 \frac{d}{d x} (sec^{- \frac{1}{2}} (x))

Apply the chain rule:

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

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

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

= 4 (- \frac{1}{2 ( sec ( x ) ) ^{\frac{3}{2}}} sec (x) tan (x))

Simplify

4 (- \frac{1}{2 sec ^{\frac{3}{2}} ( x )} sec (x) tan (x)) : - 2 tan (x) cos^{\frac{1}{2}} (x)

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

\int_{- 1}^{5} (1 + 4 x) d x

y^{^{''}} - 4 y^{^{'}} + 9 y = x e^{x}

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

f (x) = \frac{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}}

4 x, 2 x

What is the derivative of 4/(sqrt(sec(x))) ?
The derivative of 4/(sqrt(sec(x))) is -2tan(x)cos^{1/2}(x)
What is the first derivative of 4/(sqrt(sec(x))) ?
The first derivative of 4/(sqrt(sec(x))) is -2tan(x)cos^{1/2}(x)