What is the derivative of-3sin(sin(3x)cos(3x)) ?

The derivative of-3sin(sin(3x)cos(3x)) is -3(3cos^2(3x)cos(sin(3x))-3sin(3x)sin(sin(3x)))

What is the first derivative of-3sin(sin(3x)cos(3x)) ?

The first derivative of-3sin(sin(3x)cos(3x)) is -3(3cos^2(3x)cos(sin(3x))-3sin(3x)sin(sin(3x)))

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Popular >

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

- 3 (3 cos^{2} (3 x) cos (sin (3 x)) - 3 sin (3 x) sin (sin (3 x)))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

- 3 (cos (sin (3 x)) cos (3 x) \cdot 3 cos (3 x) + (- sin (3 x) \cdot 3) sin (sin (3 x))) : - 3 (3 cos^{2} (3 x) cos (sin (3 x)) - 3 sin (3 x) sin (sin (3 x)))

= - 3 (3 cos^{2} (3 x) cos (sin (3 x)) - 3 sin (3 x) sin (sin (3 x)))

\int_{0}^{2} (x^{2} + 1) d x

\frac{d}{d x} (x^{5} - 3 x^{4} + \frac{4}{3 x ^{2}} + \frac{5}{x ^{3}})

\frac{d}{d x} (2 \cdot cos (2 x))

\frac{\partial}{\partial x} (cos (π x) - x^{2} y + e^{x z} + yz)

f (x) = - e^{x} x + 2 e^{x}

What is the derivative of-3sin(sin(3x)cos(3x)) ?
The derivative of-3sin(sin(3x)cos(3x)) is -3(3cos^2(3x)cos(sin(3x))-3sin(3x)sin(sin(3x)))
What is the first derivative of-3sin(sin(3x)cos(3x)) ?
The first derivative of-3sin(sin(3x)cos(3x)) is -3(3cos^2(3x)cos(sin(3x))-3sin(3x)sin(sin(3x)))