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Popular >

derivative of sin(3xcos(3x))

Solution

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

Solution

3 cos (6 x)

Solution steps

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

Apply the Product Rule:

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

f = sin (3 x), g = cos (3 x)

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

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

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

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

Simplify

cos (3 x) \cdot 3 cos (3 x) + (- sin (3 x) \cdot 3) sin (3 x) : 3 cos (6 x)

= 3 cos (6 x)

Graph

Popular Examples

integral of 2sqrt(cos(2x))sin(2x)

\int 2 cos (2 x) sin (2 x) d x

integral of 1/((x^2+3x+5)^3)

\int \frac{1}{( x ^{2} + 3 x + 5 ) ^{3}} d x

integral of 2/(sqrt(3x-7))

\int \frac{2}{3 x - 7} d x

limit as x approaches-6+of (2x)/(6+x)

x \to - 6 + lim (\frac{2 x}{6 + x})

(\partial)/(\partial x)(((1+y))/((1+x)))

\frac{\partial}{\partial x} (\frac{( 1 + y )}{( 1 + x )})

Frequently Asked Questions (FAQ)

What is the derivative of sin(3xcos(3x)) ?
The derivative of sin(3xcos(3x)) is 3cos(6x)
What is the first derivative of sin(3xcos(3x)) ?
The first derivative of sin(3xcos(3x)) is 3cos(6x)