What is the derivative of axcos(3x) ?

The derivative of axcos(3x) is a(cos(3x)-3xsin(3x))

What is the first derivative of axcos(3x) ?

The first derivative of axcos(3x) is a(cos(3x)-3xsin(3x))

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\frac{d}{d x} (a x cos (3 x))

a (cos (3 x) - 3 x sin (3 x))

Solution steps

\frac{d}{d x} (a x cos (3 x))

Take the constant out:

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

= a \frac{d}{d x} (x cos (3 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (3 x)

= a (\frac{d x}{d x} cos (3 x) + \frac{d}{d x} (cos (3 x)) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= a (1 \cdot cos (3 x) + (- sin (3 x) \cdot 3) x)

Simplify

= a (cos (3 x) - 3 x sin (3 x))

n = 1 \sum \infty \frac{1}{2 ^{n} + 3 ^{n}}

x y^{2} (\frac{d y}{d x}) = y^{3} - x^{3}

\int (2 x y^{2} + 2 y) d x

x y^{^{'}} + 2 y = 3 x

y = 2 - x^{2}, y = - x

What is the derivative of axcos(3x) ?
The derivative of axcos(3x) is a(cos(3x)-3xsin(3x))
What is the first derivative of axcos(3x) ?
The first derivative of axcos(3x) is a(cos(3x)-3xsin(3x))