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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{3} \cdot 3 tan^{2} (x) sec^{2} (x) : tan^{2} (x) sec^{2} (x)

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

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