What is the derivative of ax+cot(ax) ?

The derivative of ax+cot(ax) is -acot^2(ax)

What is the first derivative of ax+cot(ax) ?

The first derivative of ax+cot(ax) is -acot^2(ax)

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\frac{d}{d x} (a x + cot (a x))

- a cot^{2} (a x)

Solution steps

\frac{d}{d x} (a x + cot (a x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a x) + \frac{d}{d x} (cot (a x))

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

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

= a - csc^{2} (a x) a

Simplify

a - csc^{2} (a x) a : - a cot^{2} (a x)

= - a cot^{2} (a x)

y^{^{''}} + 16 y = 40 sec (4 t)

x \to - 4 + lim (\frac{- 4 x}{x + 4})

f (x) = 2 sin^{2} (x)

\frac{\partial}{\partial x} (7 y e^{x})

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{2 y}, y (0) = - 7

What is the derivative of ax+cot(ax) ?
The derivative of ax+cot(ax) is -acot^2(ax)
What is the first derivative of ax+cot(ax) ?
The first derivative of ax+cot(ax) is -acot^2(ax)