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Popular >

derivative of 1/(sec^2(4x))

Solution

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

Solution

- 4 sin (8 x)

Solution steps

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

Simplify

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

= \frac{d}{d x} (cos^{2} (4 x))

Apply the chain rule:

2 cos (4 x) \frac{d}{d x} (cos (4 x))

= 2 cos (4 x) \frac{d}{d x} (cos (4 x))

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= 2 cos (4 x) (- sin (4 x) \cdot 4)

Simplify

2 cos (4 x) (- sin (4 x) \cdot 4) : - 4 sin (8 x)

= - 4 sin (8 x)

Popular Examples

derivative of f(x)=ln(6)-3x^5 derivative of

f (x) = ln (6) - 3 x^{5}

derivative of (x^2)/(x^2+1)derivative of

\frac{x ^{2}}{x ^{2} + 1}

limit as x approaches infinity of 52.2+(41.9*e^{(-0.055*x)})

x \to \infty lim (52.2 + (41.9 \cdot e^{(- 0.055 \cdot x)}))

derivative of ln(x^2+y)

\frac{d}{d x} (ln (x^{2} + y))

integral of 1/(3cos(x)+4sin(x))

\int \frac{1}{3 cos ( x ) + 4 sin ( x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of 1/(sec^2(4x)) ?
The derivative of 1/(sec^2(4x)) is -4sin(8x)
What is the first derivative of 1/(sec^2(4x)) ?
The first derivative of 1/(sec^2(4x)) is -4sin(8x)