What is the derivative of (d/(dx(ln(cos(x))))^2) ?

The derivative of (d/(dx(ln(cos(x))))^2) is 2sec^2(x)tan(x)

What is the first derivative of (d/(dx(ln(cos(x))))^2) ?

The first derivative of (d/(dx(ln(cos(x))))^2) is 2sec^2(x)tan(x)

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

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

Solution steps

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

Apply the chain rule:

2 \frac{d}{d x} (ln (cos (x))) \frac{d}{d x} (\frac{d}{d x} (ln (cos (x))))

= 2 \frac{d}{d x} (ln (cos (x))) \frac{d}{d x} (\frac{d}{d x} (ln (cos (x))))

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x - 39}{x ^{2} - x - 12} d x

\int_{0}^{1} \frac{4 t ^{3}}{1 + t ^{4}} d t

y^{^{''}} + 9 y = 0, y (0) = - 6, y^{^{'}} (0) = - 9

\frac{d}{d x} (\frac{- 8 x}{( x ^{2} - 4 ) ^{2}})

\int_{0}^{1} \frac{1}{e ^{x}} d x

What is the derivative of (d/(dx(ln(cos(x))))^2) ?
The derivative of (d/(dx(ln(cos(x))))^2) is 2sec^2(x)tan(x)
What is the first derivative of (d/(dx(ln(cos(x))))^2) ?
The first derivative of (d/(dx(ln(cos(x))))^2) is 2sec^2(x)tan(x)