What is the derivative of 6x-tan(6x) ?

The derivative of 6x-tan(6x) is -6tan^2(6x)

What is the first derivative of 6x-tan(6x) ?

The first derivative of 6x-tan(6x) is -6tan^2(6x)

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\frac{d}{d x} (6 x - tan (6 x))

- 6 tan^{2} (6 x)

Solution steps

\frac{d}{d x} (6 x - tan (6 x))

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (6 x) = 6

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

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

Simplify

6 - sec^{2} (6 x) \cdot 6 : - 6 tan^{2} (6 x)

= - 6 tan^{2} (6 x)

What is the derivative of 6x-tan(6x) ?
The derivative of 6x-tan(6x) is -6tan^2(6x)
What is the first derivative of 6x-tan(6x) ?
The first derivative of 6x-tan(6x) is -6tan^2(6x)