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

The derivative of 1/3 tan^3(x+tan^2(2x)) is tan^2(x)sec^2(x)+4sec^2(2x)tan(2x)

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

The first derivative of 1/3 tan^3(x+tan^2(2x)) is tan^2(x)sec^2(x)+4sec^2(2x)tan(2x)

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

tan^{2} (x) sec^{2} (x) + 4 sec^{2} (2 x) tan (2 x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (tan^{2} (2 x)) = 4 sec^{2} (2 x) tan (2 x)

= tan^{2} (x) sec^{2} (x) + 4 sec^{2} (2 x) tan (2 x)

\int \frac{1}{u ^{2} + 1} d u

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

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

\int cos (t^{3}) d t

What is the derivative of 1/3 tan^3(x+tan^2(2x)) ?
The derivative of 1/3 tan^3(x+tan^2(2x)) is tan^2(x)sec^2(x)+4sec^2(2x)tan(2x)
What is the first derivative of 1/3 tan^3(x+tan^2(2x)) ?
The first derivative of 1/3 tan^3(x+tan^2(2x)) is tan^2(x)sec^2(x)+4sec^2(2x)tan(2x)