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Popular >

derivative of 2sec^2(2x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (sec (2 x)) = sec (2 x) tan (2 x) \cdot 2

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

Simplify

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

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

Popular Examples

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5 (2 x cos (3 x) - 3 x^{2} sin (3 x))

y^{^{'}} = - \frac{2 y}{x}

derivative of x^3+3x+1

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

(\partial)/(\partial x)(9x^2-7)

\frac{\partial}{\partial x} (9 x^{2} - 7)

integral of x^3*5^{-x}

\int x^{3} \cdot 5^{- x} d x

Frequently Asked Questions (FAQ)

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