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

The derivative of cos(x-5tan(x)) is -sin(x)-5sec^2(x)

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

The first derivative of cos(x-5tan(x)) is -sin(x)-5sec^2(x)

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

- sin (x) - 5 sec^{2} (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

\frac{d}{d x} (5 tan (x)) = 5 sec^{2} (x)

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

What is the derivative of cos(x-5tan(x)) ?
The derivative of cos(x-5tan(x)) is -sin(x)-5sec^2(x)
What is the first derivative of cos(x-5tan(x)) ?
The first derivative of cos(x-5tan(x)) is -sin(x)-5sec^2(x)