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

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

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

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

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derivative of

f (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}

sin (- 5 x)

\int \frac{1}{cos ( u ) + 1} d u

\frac{d y}{d x} = 6 x 8 y + 17

\frac{d y}{d x} = x^{2} + \frac{y}{x}

\int \frac{- 1}{1 + sin ( x )} d x

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