What is the derivative of tan(6x+x^{-4}) ?

The derivative of tan(6x+x^{-4}) is sec^2(6x)*6-4/(x^5)

What is the first derivative of tan(6x+x^{-4}) ?

The first derivative of tan(6x+x^{-4}) is sec^2(6x)*6-4/(x^5)

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\frac{d}{d x} (tan (6 x) + x^{- 4})

sec^{2} (6 x) \cdot 6 - \frac{4}{x ^{5}}

Solution steps

\frac{d}{d x} (tan (6 x) + x^{- 4})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (tan (6 x)) + \frac{d}{d x} (x^{- 4})

\frac{d}{d x} (tan (6 x)) = sec^{2} (6 x) \cdot 6

\frac{d}{d x} (x^{- 4}) = - \frac{4}{x ^{5}}

= sec^{2} (6 x) \cdot 6 - \frac{4}{x ^{5}}

What is the derivative of tan(6x+x^{-4}) ?
The derivative of tan(6x+x^{-4}) is sec^2(6x)*6-4/(x^5)
What is the first derivative of tan(6x+x^{-4}) ?
The first derivative of tan(6x+x^{-4}) is sec^2(6x)*6-4/(x^5)