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Popular Calculus >

derivative of (3cos(2x+sin(3x)+4)^2)

Solution

\frac{d}{d x} ((3 cos (2 x) + sin (3 x) + 4)^{2})

Solution

2 (3 cos (2 x) + sin (3 x) + 4) (3 cos (3 x) - 6 sin (2 x))

Solution steps

\frac{d}{d x} ((3 cos (2 x) + sin (3 x) + 4)^{2})

Apply the chain rule:

2 (3 cos (2 x) + sin (3 x) + 4) \frac{d}{d x} (3 cos (2 x) + sin (3 x) + 4)

= 2 (3 cos (2 x) + sin (3 x) + 4) \frac{d}{d x} (3 cos (2 x) + sin (3 x) + 4)

\frac{d}{d x} (3 cos (2 x) + sin (3 x) + 4) = 3 cos (3 x) - 6 sin (2 x)

= 2 (3 cos (2 x) + sin (3 x) + 4) (3 cos (3 x) - 6 sin (2 x))

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (3cos(2x+sin(3x)+4)^2) ?
The derivative of (3cos(2x+sin(3x)+4)^2) is 2(3cos(2x)+sin(3x)+4)(3cos(3x)-6sin(2x))
What is the first derivative of (3cos(2x+sin(3x)+4)^2) ?
The first derivative of (3cos(2x+sin(3x)+4)^2) is 2(3cos(2x)+sin(3x)+4)(3cos(3x)-6sin(2x))