What is the derivative of a+bxcos(3x+cxsin(3x)) ?

The derivative of a+bxcos(3x+cxsin(3x)) is b(-3xsin(3x)+cos(3x))+c(3xcos(3x)+sin(3x))

What is the first derivative of a+bxcos(3x+cxsin(3x)) ?

The first derivative of a+bxcos(3x+cxsin(3x)) is b(-3xsin(3x)+cos(3x))+c(3xcos(3x)+sin(3x))

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\frac{d}{d x} (a + b x cos (3 x) + c x sin (3 x))

b (- 3 x sin (3 x) + cos (3 x)) + c (3 x cos (3 x) + sin (3 x))

Solution steps

\frac{d}{d x} (a + b x cos (3 x) + c x sin (3 x))

Apply the Sum/Difference Rule:

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

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

\frac{d a}{d x} = 0

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

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

= 0 + b (cos (3 x) - 3 x sin (3 x)) + c (sin (3 x) + 3 x cos (3 x))

Simplify

= b (- 3 x sin (3 x) + cos (3 x)) + c (3 x cos (3 x) + sin (3 x))

\frac{\partial}{\partial x} (2 x y - 2 y)

\frac{\partial}{\partial y} (\frac{1}{1 + x ^{2} + y ^{2}})

\frac{d}{d x} (x^{2} x^{3} + a^{3})

\int \frac{3 x ^{3} + 3 x + 2}{x ^{3} + x} d x

f (x) = \frac{1}{x ^{4}}, at x = 3

What is the derivative of a+bxcos(3x+cxsin(3x)) ?
The derivative of a+bxcos(3x+cxsin(3x)) is b(-3xsin(3x)+cos(3x))+c(3xcos(3x)+sin(3x))
What is the first derivative of a+bxcos(3x+cxsin(3x)) ?
The first derivative of a+bxcos(3x+cxsin(3x)) is b(-3xsin(3x)+cos(3x))+c(3xcos(3x)+sin(3x))