What is the first (3cos(x))^' ?

The first (3cos(x))^' is -3sin(x)

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(3cos(x))^'

(3 cos (x))^{^{'}}

- 3 sin (x)

Solution steps

(3 cos (x))^{'}

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 (cos (x))^{^{'}}

Apply the common derivative:

(cos (x))^{'} = - sin (x)

= 3 (- sin (x))

Simplify

= - 3 sin (x)

\frac{\partial}{\partial x} (x^{3} y^{2} - 2 x e^{x y})

\int cot (y) csc^{2} (y) d y

y^{^{''}} - 4 y^{^{'}} + 3 y = x

y^{^{'}} - \frac{6}{x} y = \frac{y ^{4}}{x ^{3}}

x \to 0 lim (\frac{arcsin ( x )}{7 x})