What is the derivative of sin(xcos(2x)) ?

The derivative of sin(xcos(2x)) is -5cos(x)+6cos^3(x)

What is the first derivative of sin(xcos(2x)) ?

The first derivative of sin(xcos(2x)) is -5cos(x)+6cos^3(x)

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

- 5 cos (x) + 6 cos^{3} (x)

Solution steps

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

Apply the Product Rule:

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

f = sin (x), g = cos (2 x)

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

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

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

= cos (x) cos (2 x) + (- sin (2 x) \cdot 2) sin (x)

Simplify

cos (x) cos (2 x) + (- sin (2 x) \cdot 2) sin (x) : - 5 cos (x) + 6 cos^{3} (x)

= - 5 cos (x) + 6 cos^{3} (x)

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

\frac{d}{d x} (24 x^{\frac{3}{2}})

s im pl i f y \frac{2 x}{x ^{2} + 1}

f (x) = x 2

\int \frac{( ln ( z ) ) ^{6}}{z} d z

What is the derivative of sin(xcos(2x)) ?
The derivative of sin(xcos(2x)) is -5cos(x)+6cos^3(x)
What is the first derivative of sin(xcos(2x)) ?
The first derivative of sin(xcos(2x)) is -5cos(x)+6cos^3(x)