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Popular >

derivative of sec^2(4x)

Solution

derivative of

sec^{2} (4 x)

Solution

8 sec^{2} (4 x) tan (4 x)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (sec (4 x)) = sec (4 x) tan (4 x) \cdot 4

= 2 sec (4 x) sec (4 x) tan (4 x) \cdot 4

Simplify

2 sec (4 x) sec (4 x) tan (4 x) \cdot 4 : 8 sec^{2} (4 x) tan (4 x)

= 8 sec^{2} (4 x) tan (4 x)

Popular Examples

(\partial)/(\partial x)(x^{8/x})

\frac{\partial}{\partial x} (x^{\frac{8}{x}})

integral of (12x^3-1)/(3x^4-x+10)

\int \frac{12 x ^{3} - 1}{3 x ^{4} - x + 10} d x

integral of ((e^x+e^{-x}))/(e^x-e^{-x)}

\int \frac{( e ^{x} + e ^{- x} )}{e ^{x} - e ^{- x}} d x

integral of ((x-1)^2)/(x^2)

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

area 3cos(8x),3-3cos(8x),[0, pi/8 ]area

3 cos (8 x), 3 - 3 cos (8 x), [0, \frac{π}{8}]

Frequently Asked Questions (FAQ)

What is the derivative of sec^2(4x) ?
The derivative of sec^2(4x) is 8sec^2(4x)tan(4x)
What is the first derivative of sec^2(4x) ?
The first derivative of sec^2(4x) is 8sec^2(4x)tan(4x)