What is the derivative of-tan(x-5cot(x)) ?

The derivative of-tan(x-5cot(x)) is -sec^2(x)+5csc^2(x)

What is the first derivative of-tan(x-5cot(x)) ?

The first derivative of-tan(x-5cot(x)) is -sec^2(x)+5csc^2(x)

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\frac{d}{d x} (- tan (x) - 5 cot (x))

- sec^{2} (x) + 5 csc^{2} (x)

Solution steps

\frac{d}{d x} (- tan (x) - 5 cot (x))

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (tan (x)) - \frac{d}{d x} (5 cot (x))

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

\frac{d}{d x} (5 cot (x)) = - 5 csc^{2} (x)

= - sec^{2} (x) - (- 5 csc^{2} (x))

Simplify

= - sec^{2} (x) + 5 csc^{2} (x)

What is the derivative of-tan(x-5cot(x)) ?
The derivative of-tan(x-5cot(x)) is -sec^2(x)+5csc^2(x)
What is the first derivative of-tan(x-5cot(x)) ?
The first derivative of-tan(x-5cot(x)) is -sec^2(x)+5csc^2(x)