What is the derivative of sin(3xsin^3(x)+cos(3x)cos^3(x)) ?

The derivative of sin(3xsin^3(x)+cos(3x)cos^3(x)) is -3sin(4x)cos(2x)

What is the first derivative of sin(3xsin^3(x)+cos(3x)cos^3(x)) ?

The first derivative of sin(3xsin^3(x)+cos(3x)cos^3(x)) is -3sin(4x)cos(2x)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= 3 sin^{2} (x) sin (4 x) - 3 cos^{2} (x) sin (4 x)

Simplify

3 sin^{2} (x) sin (4 x) - 3 cos^{2} (x) sin (4 x) : - 3 sin (4 x) cos (2 x)

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

y = - 16 x^{2} + 165 x + 69

y = 3 x + 21

y = x^{3} - 3 x^{2} - 45 x + 2

f (y) = 3 - 2 y

f (n) = n^{2} + 8 n + 15

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