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Popular >

derivative of axcos(2x+bxsin(2x))

Solution

\frac{d}{d x} (a x cos (2 x) + b x sin (2 x))

Solution

a (cos (2 x) - 2 x sin (2 x)) + b (sin (2 x) + 2 x cos (2 x))

Solution steps

\frac{d}{d x} (a x cos (2 x) + b x sin (2 x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a x cos (2 x)) + \frac{d}{d x} (b x sin (2 x))

\frac{d}{d x} (a x cos (2 x)) = a (cos (2 x) - 2 x sin (2 x))

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

= a (cos (2 x) - 2 x sin (2 x)) + b (sin (2 x) + 2 x cos (2 x))

Popular Examples

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Frequently Asked Questions (FAQ)

What is the derivative of axcos(2x+bxsin(2x)) ?
The derivative of axcos(2x+bxsin(2x)) is a(cos(2x)-2xsin(2x))+b(sin(2x)+2xcos(2x))
What is the first derivative of axcos(2x+bxsin(2x)) ?
The first derivative of axcos(2x+bxsin(2x)) is a(cos(2x)-2xsin(2x))+b(sin(2x)+2xcos(2x))