What is the derivative of (1+tan(2x)^3) ?

The derivative of (1+tan(2x)^3) is 6sec^2(2x)(1+tan(2x))^2

What is the first derivative of (1+tan(2x)^3) ?

The first derivative of (1+tan(2x)^3) is 6sec^2(2x)(1+tan(2x))^2

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\frac{d}{d x} ((1 + tan (2 x))^{3})

6 sec^{2} (2 x) (1 + tan (2 x))^{2}

Solution steps

\frac{d}{d x} ((1 + tan (2 x))^{3})

Apply the chain rule:

3 (1 + tan (2 x))^{2} \frac{d}{d x} (1 + tan (2 x))

= 3 (1 + tan (2 x))^{2} \frac{d}{d x} (1 + tan (2 x))

\frac{d}{d x} (1 + tan (2 x)) = 2 sec^{2} (2 x)

= 3 (1 + tan (2 x))^{2} \cdot 2 sec^{2} (2 x)

Simplify

= 6 sec^{2} (2 x) (1 + tan (2 x))^{2}

\frac{d}{d t} (t e^{5 t})

\frac{\partial}{\partial x} (2 x^{4} y + 1)

\int_{1}^{2} 3^{- x} d x

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

\frac{d}{d x} (\frac{3 - x}{2})

What is the derivative of (1+tan(2x)^3) ?
The derivative of (1+tan(2x)^3) is 6sec^2(2x)(1+tan(2x))^2
What is the first derivative of (1+tan(2x)^3) ?
The first derivative of (1+tan(2x)^3) is 6sec^2(2x)(1+tan(2x))^2