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

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

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

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

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

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

Solution steps

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

Simplify

2 tan (x) + 2 tan^{3} (x) : 2 sec^{3} (x) sin (x)

= \frac{d}{d x} (2 sec^{3} (x) sin (x))

Take the constant out:

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

= 2 \frac{d}{d x} (sec^{3} (x) sin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec^{3} (x), g = sin (x)

= 2 (\frac{d}{d x} (sec^{3} (x)) sin (x) + \frac{d}{d x} (sin (x)) sec^{3} (x))

\frac{d}{d x} (sec^{3} (x)) = 3 sec^{3} (x) tan (x)

\frac{d}{d x} (sin (x)) = cos (x)

= 2 (3 sec^{3} (x) tan (x) sin (x) + cos (x) sec^{3} (x))

Simplify

2 (3 sec^{3} (x) tan (x) sin (x) + cos (x) sec^{3} (x)) : 2 sec^{2} (x) (1 + 3 tan^{2} (x))

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

\frac{4 s - 1}{s ^{2} ( s + 1 ) ^{3}}

x \to + 5 lim (\frac{x + 1}{x - 5})

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

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

y \cdot \frac{d y}{d x} - x = 5 y^{2}

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